Rockfish Historical Harvest Estimates

This project seeks to estimate sport fish harvest and releases of rockfish in Alaska waters by improving on the Howard et al. (2020) methods and expand the time series back to 1977 when the statewide harvest survey (SWHS) was first implemented. This is essentially a Bayesian version of the Howard methods that allows for more appropriate and defensible sharing of information between areas, handles missing data in a more appropriate manor, accurately propagates uncertainty throughout the estimation procedure and replaces the Howard decision tree approach to low sample sizes with a hierarchical model. The methods and results for generating harvest estimates are generally consistent between the Bayesian model and the Howard methods. Harvest estimates are consistent with Howard estimates during contemporary times, but may differ based on more appropriate weighting of SWHS and logbook data, including estimating and correcting bias in the SWHS data.

The Bayesian methods depart from the Howard method in how releases are estimated. The Howard methods assume that the species composition of the harvests are equal to the species composition of released fish, which is clearly contraindicated in the logbook data. For instance, logbook data demonstrates that yelloweye have been retained at high levels up until restrictions were enacted in recent years, whereas pelagic rockfish were released in significant numbers in the past with retention increasing in recent years as they have become more prized by anglers. Recent prohibition on retaining yelloweye in Southeast Alaska highlights the shortcomings of the original Howard assumptions as the species composition of the harvest would indicate that no yelloweye were caught and released during the closure.

The Howard method for estimating releases for private anglers also relied on an expansion of the logbook release estimates based on the ratio of private:guided releases of all rockfish in the SWHS. In addition to the faulty assumptions about species composition, this method ignores potential bias in SWHS estimates of harvests and releases or at least assumes that the bias in release and harvests are the same. As demonstrated in Figure 1, the bias in those two quantities appears to be quite different based on the logbook data. The Bayesian model thus attempts to estimate release probabilities based on the logbook data coupled with bias corrected estimates from the SWHS.

Lastly, the Howard methods were only used on data beginning in 1999 with the advent of the logbook program and estimates of harvests and releases prior to that have been based on linear ramps from 1999 back to the perceived start of the fishery. The Bayesian methods allow us to expand the time series back to 1977 when the SWHS was implemented by leveraging regional data trends in species composition and the proportion of caught rockfish harvested by species and/or species complex. Key advantages of the Bayesian approach are highlighted in table 1.

Table 1. Summary of key improvements in reconstructiing sport fish removals of rockfish using the Bayesian model as compared to the Howard et al. (2020) methods.

Issue	Howard	Bayes
Time series	1999 - present	1977 - present
Bias in SWHS	Not explicitly dealt with. Relies on logbook data and ratios of guided/unguided from SWHS data to estimate unguided releases and harvests.	Explicitly estimates bias in SWHS harvest and release estimates based on logbook data.
Species composition of releases	Assumes that species composition of releases is equal to that of the harvest, which is not evident in the logbook data.	Recognizes different release probabilities by species / species assemblage and estimates it from logbook data and bias corrected SWHS data
Sample size limitations	Uses sample size threshholds such that when areas fall below those threshholds values are borrowed from nearby areas.	Uses a hierarchichacal modelling approach that shares information between areas in the same region. Thus all data is used, even with small sample sizes. This is a more sound method that avoids assumptions and uses all of the data.
Error propogation	Error is propogated when variance estimates are available, but there is uncertainty associated with borrowing values from nearby areas, or the assumption of species compositions being identical in harvest and releases, are not dealt with.	By breaking the assumption that species composition is equal between harvests and releases, uncertainty in the release estimates is more reflective of the fishery. Furthermore, the hyerarchichal approach more accurately captures uncertainy within and between areas within a region.

Data

Harvest data was available for 22 commercial fishing management areas in Southcentral and Southeast Alaska. Areas with negligible rockfish harvest were pooled with adjacent areas for analysis. Specifically the Aleutian and Bering areas were pooled into an area labeled BSAI; the IBS and EKYT were pooled into an area labeled EKYKT; the Southeast, Southwest, SAKPEN and Chignik areas were pooled into an area labeled SOKO2PEN and the Westside and Mainland areas were pooled into an area labeled WKMA.

Stateside Harvest Survey (SWHS)

Statewide harvest survey estimates of rockfish catch and harvest are available for 28 years (1996-2023) for all users and for 13 years (2011-2023) for guided anglers (Figure 0). Additionally, there are overall harvest estimates from 1977- 1995 and release estimates from 1990-1995 that required some partitioning to ascribe to current management units. Harvests in unknown areas were apportioned based on harvest proportions in 1996. Variance estimates are not available for pre-1996 data and as such, the maximum observed coefficient of variation (cv) in each commercial fisheries management unit was applied to the pre-1996 values.

Figure 1.- Data sources for estimating rockfish harvests and releases in ADF&G commercial fisheries management units. Note that initial rockfish harvest estimates were not differentiated into species assemblage or species until 1998 when logbooks began differentiating by pelagic and non-pelagic. Logbooks began to collect data on yelloweye beginning in 2006. Port sampling programs to gather data on species composition of harvests began in 1996 in Southcentral and Kodiak and in 2006 in Southeast.

SWHS estimates are believed to be biased to some degree. These modelling efforts aim to estimate and correct for that bias with the assumption that logbook records are a census of guided harvests and releases.

SWHS Rockfish release estimates are inferred from the difference between catch and harvest estimates.

Adam noted that the first 5 years (23 years counting the historical data) in the SWHS data set for PWSO seem unreasonable (close to zero and not corroborated with logbook estimates). Adam recommended setting these harvests to unknown, but current model development has included the data. Once a satisfactory model has been identified we will exam the effects of censoring the PWSO data.

Creel Surveys

NA

Guide Logbooks

Sport fishing guides have been required to report their harvest of rockfish for 26 years (1998-2023). Reported harvest is also available by assemblage (pelagic vs. non-pelagic). Harvest of yelloweye and “other” (non-pelagic, non-yelloweye) rockfish were reported separately beginning in 2006.

Logbooks also record the number of rockfish released for the same categories. However, the reliability of the release data is somewhat questionable as reported releases are generally far lower than that estimated by the SWHS. As such several treatments of the data are considered.

Logbook versus SWHS estimates

Estimates of guided harvests and releases from the SWHS do not align with the census from charter logbooks. Logbook harvest reports are generally considered reliable and are used to assess the bias in SWHS reports. However, there is even greater disparity between release estimates in the two sources and it is debatable whether logbook releases should be treated as a census. The Howard et al. (2020) methods do treat the logbook release data as “true” and thus are considerably less than would be estimated from the SWHS data.

Figure 2.- SWHS harvest (left) and release (right) estimates from guided trips (x-axis) versus repoted harvests from charter logbooks (y-axis).

A note on model development

To evaluate the discrepancy in apparent bias in harvest and release data, several models were explored to estimate releases during model development. One method (\(LB_{fit}\)) considers the logbook release data to be reliable and a second method (\(LB_{cens}\)) treated the logbook release data as estimates of the minimum released, thus giving more weight to SWHS release estimates. A third method (\(LB_{hyb}\)) is a hybrid approach that treats reported releases of yelloweye as reliable but total rockfish and pelagic rockfish releases as minimums. Model development revealed a tension between the total and pelagic logbook releases and the yelloweye logbook releases. This tensions eventually highlighted the different release/retention probabilities between yelloweye and pelagics in the logbook data and prompted the current approach whereby that probability was calculated for the three main species complexes covered in the data: pelagics, yelloweye, and “other”. The methods described here follow the (\(LB_{fit}\)) formulation. Based on model behavior it is unlikely that the (\(LB_{cens}\)) model would work as there would not be enough data to estimate release probabilities. However, it may be worth running the (\(LB_{hyb}\)) approach as a sensitivity test at the very least.

Composition data

Harvest sampling data exists from Gulf of Alaska areas since 1996 and from Southeast Alaska areas since 2006. Port sampling data is comprised of the number of total rockfish, pelagic and non-pelagic rockfish, black rockfish and yelloweye rockfish. In Southeast Alaska, the number of Demersal Shelf Rockfish (DSR, of which yelloweye are one species) and slope rockfish are also recorded.

Process equations

The true harvest \(H_{ay}\) of rockfish for area \(a\) during year \(y\) is assumed to follow a temporal trend defined by a penalized spline:

\[\begin{equation} \textrm{log}(H_{ay})~\sim~\textrm{Normal}(f(a,y), {\sigma_H}) \end{equation}\]

where \(f(a,y)\) in a p-spline basis with 7 components (knots) and a second degree penalty. The variance, \(\sigma_H\), was given a normal prior with a mean and standard deviation of 0.25 and 1, respectively.

Charter and private harvest \(H_{ayu}\) (where u = 1 for charter anglers and u = 2 for private anglers) is a fraction of total annual harvest in each area:

\[\begin{equation} H_{ay1}~=~H_{ay}P_{(user)ay1}\\H_{ay2}~=~H_{ay}(1-P_{(user)ay1}) \end{equation}\]

where \(P_{(user)ay1}\) is the fraction of the annual harvest in each area taken by charter anglers. \(P_{(user)ay1}\) was modeled hierarchically across years as:

\[\begin{equation} P_{(user)ay1}~\sim~\textrm{beta}(\lambda1_a, \lambda2_a) \end{equation}\]

with non-informative priors on both parameters.

Annual black rockfish harvest \(H_{(black)ayu}\) for each area and user group is:

\[\begin{equation} H_{(black)ayu}~=~H_{ayu}P_{(pelagic)ayu}P_{(black|pelagic)ayu} \end{equation}\]

where \(P_{(pelagic)ayu}\) is the fraction of the annual harvest for each area and user group that was pelagic rockfish and \(P_{(black|pelagic)ayu}\) is the fraction of the annual harvest of pelagic rockfish for each area and user group that was black rockfish.

The southeast region also tracks two other non-pelagic rockfish assemblages, demersal shelf rockfish (DSR, which includes yelloweye) and slope rockfish. For the southeast region the harvest of those two assemblages is thus

\[\begin{equation} H_{(DSR)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(DSR|non-pelagic)ayu}\\ H_{(slope)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(slope|non-pelagic)ayu}\\ \end{equation}\]

where \(P_{(DSR|non-pelagic)ayu}\) and \(P_{(slope|non-pelagic)ayu}\) are the fractions of the annual harvest of non-pelagic rockfish for each area and user group that were DSR and slope rockfish, respectively.

Annual yelloweye rockfish harvest \(H_{(yelloweye)ayu}\) for each area and user group is calculated differently for central/Kodiak areas and southeast areas. For central and Kodiak areas yelloweye rockfish harvests are calculated as

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(yelloweye|non-pelagic)ayu} \end{equation}\]

where \(P_{(yellow|non-pelagic)ayu}\) is the fraction of the annual harvest of non-pelagic rockfish for each area and user group that was yelloweye rockfish.

For southeast areas yelloweye harvests are a fraction of the DSR harvests such that

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{(DSR)ayu}P_{(yelloweye|DSR)ayu} \end{equation}\]

The composition parameters \(P_{(comp)ayu}\), were modeled using a logistic curve that would allow hindcasting without extrapolating beyond the limit of observed values such that:

\[\begin{equation} \textrm{logit}(P_{(comp)ayu})~=~\beta0_{(comp)ayu} + \frac{\beta1_{(comp)ayu}}{(1 + exp(\beta2_{(comp)ayu}*(y - \beta3_{(comp)ayu})))} + \beta4_{(comp)ayu}*I(u=private)+re_{(comp)ayu} \end{equation}\]

where the \(\beta\) parameters define the intercept, scaling factor, slope, inflection point and private angler effect, respectively, \(y\) is the year index, \(I(u=private)\) is an index variable which is 1 when the user groups is private and 0 otherwise and \(re_{(comp)ayu}\) is a random effect with a non-informative prior. \(\beta\) parameters were modeled hierarchically by region. When \(\beta\) parameters were inestimable as a result of no discernible change in composition over the observed time period. \(\beta1\) (scaling factor) and \(\beta2\) (slope) were fixed to 0 so that the long term mean value was used for hindcasting.

The true number of released rockfish \(R_{ayu}\) were based on the proportion of the total catch harvested, \(pH_{(comp)ayu}\), by area, year, user group and species grouping. Because release data from the SWHS is for all rockfish and the release data from logbooks is only subdivided into pelagics, yelloweye and “other” (non-pelagic, non-yelloweye), we only estimated \(pH_{(comp)ayu}\) for those categories. Thus, converting \(H_{(comp)ayu}\) to total catches by user group, \(C_{(comp)ayu}\), with \(pH_{(comp)ayu}\) results in estimates of total releases such that

\[\begin{equation} R_{(comp)ayu}~=~ C_{(comp)ayu} - H_{(comp)ayu} ~=~ \frac{H_{(comp)ayu}}{pH_{(comp)ayu}} - H_{(comp)ayu} \end{equation}\]

with total releases equal to the sum of the compositional releases. For non-yelloweye DSR and Slope rockfish assemblages in Southeast Alaska \(R_{(DSR)ayu}\) and \(R_{(slope)ayu}\) were estimated from \(R_{(other)ayu}\) using the species composition data from the harvest, thus assuming that slope and DSR assemblages were caught and released at the same rates.

The proportion harvest parameters for \(pH_{(comp)ayu}\) were modeled using a logistic curve that would allow hindcasting based on trends in the data without extrapolating beyond the range of observed values such that

\[\begin{equation} \textrm{logit}(pH_{(pH)ayuc})~=~\beta0_{(pH)ayu} + \frac{\beta1_{(pH)ayuc}}{(1 + exp(\beta2_{(pH)ayuc}*(y - \beta3_{(pH)ayuc})))} + \beta4_{(pH)ayuc}*I(u=private)+re_{(pH)ayuc} \end{equation}\]

A random effect term allowed estimation during the historical period when data is available, but the curve defined by the above equation determined release estimates between 1977 and 1990. As with the compositional trends, \(\beta\) parameters were modeled hierarchically by region. When \(\beta\) parameters were inestimable as a result of no discernable change in harvest probability over the observed time period, \(\beta1\) (scaling factor) and \(\beta2\) (slope) were fixed to 0 so that the long term mean value was applied.

Release mortality (i.e., the number of released rockfish expected to die) was calculated assuming fixed mortality rates developed in each of the regions. Deep water release (DWR) devices were mandated for charter fleets in 2013 and rates were derived from CITATION. Southeast applies basic rates estimated in these studies while Southcentral and Kodiak rates were derived by using historical depth-of-release data to adjust the rates based on area and user group.

The total number of mortalities by year, area, user and species/species assemblage in numbers was calculated by summing harvests and release mortality such that

\[\begin{equation} M_{(comp)ayu}~=~ H_{(comp)ayu} + m_{R-(comp)ayu} * R_{(comp)ayu} \end{equation}\]

where \(m_{R-(comp)ayu}\) is the release mortality rate by year, area, user and species (Figure XX).

Total removals in biomass were converted using the average weight of fish from port sampling?. A minimum sample size per year of X fish was used as the cutoff for including in the data set. Weights were modeled hierarchically to estimate weights in years when data was missing. The total biomass of removals by year, area, user and species was thus

\[\begin{equation} B_{(comp)ayu}~=~ \overline{wt}_{(comp)ayu} * M_{(comp)ayu} \end{equation}\]

where \(\overline{wt}_{(comp)ayu}\) is the mean weight by species, area, user and year.

Observation equations

SWHS estimates of annual rockfish harvest \(\widehat{SWHS}_H{ay}\) were assumed to index true harvest:

\[\begin{equation} \widehat{SWHS}_H{ay}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay}b_{ay}), \sigma_{SWHSHay}^2\right) \end{equation}\]

where bias in the SWHS harvest estimates \(b_H{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_H{ay}~\sim~\textrm{Normal}(\mu_H{(b)a}, \sigma_H{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

SWHS estimates of guided angler harvest \(\widehat{SWHS}_H{ay1}\) are related to total harvest by:

\[\begin{equation} \widehat{SWHS}_H{ay1}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay1}b_{ay}), \sigma_{SWHS_{ay1}}^2\right) \end{equation}\]

Reported guide logbook harvest \(\widehat{LB}_H{ay}\) is related to true harvest as:

\[\begin{equation} \widehat{LB}_H{ay}~\sim~\textrm{Poisson}(H_{ay1})\\ \widehat{LB}_H{(pelagic)ay}~\sim~\textrm{Poisson}(H_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_H{(yelloweye)ay}~\sim~\textrm{Poisson}(H_{(yelloweye)ay1})\\ \widehat{LB}_H{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(H_{(nonpel,nonye)ay1})\\ \end{equation}\]

Note that for central and Kodiak areas \(H_{(nonpel,nonye)ay1}\) is equal to the total harvest minus pelagic and yelloweye harvests. For southeast areas \(H_{(nonpel,nonye)ay1}\) is equal to the sum of the DSR and slope harvests minus yelloweye harvests.

SWHS estimates of annual rockfish releases \(\widehat{SWHS}_R{ay}\) were assumed to index true releases in a similar fashion and thus modeled similarly. As such, the release data are related to true releases just as harvests were modeled such that:

\[\begin{equation} \widehat{LB}_R{ay}~\sim~\textrm{Poisson}(R_{ay1})\\ \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{Poisson}(R_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

Because logbook release data is more questionable and demonstrates greater disagreement with SWHS estimates (Figure 1), a second approaches was considered that loosened the assumption that logbook releases were a census. Methods explored to develope \(LB_{hyb}\) and \(LB_{cens}\) models are detailed at the end of this section.

SWHS estimates of guided angler release \(\widehat{SWHS}_R{ay1}\) is modeled the same as harvests.

SWHS release bias was modeled independently of the harvest bias \(b_H{ay}\) such that

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

where bias in the SWHS release estimates \(b_R{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

The number of pelagic rockfish sampled in harvest sampling programs \(x_{(pelagic)ayu}\) follow a binomial distribution:

\[\begin{equation} x_{(pelagic)ayu}~\sim~\textrm{Binomial}(P_{(pelagic)ayu}, N_{ayu}) \end{equation}\]

where \(N_{ayu}\) is the total number of rockfish sampled in area \(a\) during year \(y\) form user group \(u\). The number of black rockfish sampled in harvest sampling programs was thus a proportion of the pelagic harvests

\[\begin{equation} x_{(black)ayu}~\sim~\textrm{Binomial}(P_{(black)ayu}, N_{ayu}^{pel}) \end{equation}\]

Yelloweye rockfish in Southcentral and Kodiak were modeled similarly as a proportion of the total number of non-pelagics such that

\[\begin{equation} x_{(yellow_{R2})ayu}~\sim~\textrm{Binomial}(P_{(yellow_{R2})ayu}, N_{ayu}^{nonpel}) \end{equation}\]

Southeast areas have several other non-pelagic groupings such that DSR and slope rockfish are a proportion of non-pelagics

\[\begin{equation} x_{(DSR)ayu}~\sim~\textrm{Binomial}(P_{(DSR)ayu}, N_{ayu}^{nonpel}) \end{equation}\]

and

\[\begin{equation} x_{(slope)ayu}~\sim~\textrm{Binomial}(P_{(slope)ayu}, N_{ayu}^{nonpel}) \end{equation}\]

with yelloweye in southeast a proportion of the DSR harvest

\[\begin{equation} x_{(yellow_{R1})ayu}~\sim~\textrm{Binomial}(P_{(yellow_{R1})ayu}, N_{ayu}^{DSR}). \end{equation}\].

Kodiak has limited port sampling beyond the main harbors but has a robust hydroacoustic survey that is used to quantify black rockfish abundance across the management area and uses stereocameras to derive species compositions of the hydroacoustic data. This data was used as supplementary data to further inform the model to the proportion of pelagic rockfish that are black in Kodiak areas. Angler landings in Kodiak show a higher proportion of black rockfish relative to the hydroacoustic survey and thus the proportion of black rockfish in the hydroacoustic sample related to the true proportion such that

\[\begin{equation} P_{(black|pelagic)ayu}^{HA} ~\sim~ P_{(black|pelagic)ayu} + ae_{au} \end{equation}\].

where \(ae_{au}\) is the angler effect for each area and user group modeled hierarchically around a mean of 0. Predicted \(P_{(black|pelagic)ayu}^{HA}\) assumed a beta distribution such that

\[\begin{equation} P_{(black|pelagic)ayu}^{HA} ~\sim~ beta(\alpha_{HA},\beta_{HA}) \end{equation}\]

where

\[\begin{equation} \alpha_{HA} ~=~ (P_{(black|pelagic)ayu}^{HA})^2 * \frac{1 - P_{(black|pelagic)ayu}^{HA}}{\frac{var_{P_{HA}}-1}{P_{(black|pelagic)ayu}^{HA}}}, \end{equation}\]

\[\begin{equation} \beta_{HA} ~=~ (\alpha_{HA}) * \frac{1}{P_{(black|pelagic)ayu}^{HA} - 1}, \end{equation}\]

\[\begin{equation} var_{P_{HA}} ~=~ (P_{(black|pelagic)ayu}^{HA} * cvP_{(black|pelagic)ayu}^{HA})^2 \end{equation}\]

where \(cvP_{(black|pelagic)ayu}^{HA}\) is the coefficient of variation for the hydroacoustic proportions

\[\begin{equation} cvP_{(black|pelagic)ayu}^{HA} ~=~ \frac{\sqrt{varP_{(black|pelagic)ayu}^{HA}}}{P_{(black|pelagic)ayu}^{HA}} \end{equation}\]

and the variance is approximated using the XXXX method as

\[\begin{equation} varP_{(black|pelagic)ayu}^{HA} ~=~ (\frac{1}{n_{pel}})^2 * varN_{black} + (\frac{n_{black}}{n_{pel}^2}) * varN_{pel} \end{equation}\]

where \(varN_{black}\) and \(varN_{black}\) are the variance of the estimated number of black and pelagic rockfish in the hydroacoustic survey, respectively (CITATION).

The average weight of rockfish by species, user, area and year was modeled hierarchically at several levels within regions such that

\[\begin{equation} wt_{(comp)ayu} ~\sim~ Normal(wt_{(comp)au},\sigma_{wt_{(comp)au}}) ~\sim~ Normal(wt_{(comp)a},\sigma_{wt_{(comp)a}}) ~\sim~ Normal(wt_{(comp)region},\sigma_{wt_{(comp)region}}) \end{equation}\]

where region refers to Kodiak, Southcentral and Southeast. Mean weights and variance were calculated as XXX.

Alternative likelihoods for release estimates

To loosen the assumption that logbook release data are an effective census of true releases I explored models that treated logbook release estimates as a lower bound on the estimate of true releases. In a hybrid approach yelloweye and non-pelagic releases are regarded as a reliable census (given the emphasis and ease of recording these fish) but censors the pelagic and total rockfish release estimates (where censoring implies NA values) such that

\[\begin{equation} \text{censored} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), 1\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right) \\ \text{censored} \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right) \\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

This model formulation failed such that there was not enough data to inform pelagic releases and the values did not seem valid. A second approach is being explored that fits the censored data using a lognormal distribution centered around the logbook release value, but also with a lower bound equal to the number of recorded releases such that

\[\begin{equation} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), \sigma_{Ray1}^2\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right) \\ \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), \sigma_{Ray1}^2\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right) \\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

Logbook data is assumed to be a census and as such there is no estimate of uncertainty. As of this writing, several methods are being examined for how to treat \(\sigma_{Ray1}^2\). Models are being run that attempt to allow the model to estimate \(\sigma_{Ray1}^2\) with priors. A simple model applies a uniform prior (0.1,50) to \(\sigma_{Ray1}^2\). A hierarchichal approach based on regions is also being examined whereby \(\sigma_{Ray1}^2\) is lognormally distributed around hyper priors \(\mu_{\sigma_R}\) and \(\sigma_{\sigma_R}\). Initial efforts have applied a uniform prior on \(\mu_{\sigma_R}\) between 1 and 50 and on \(\sigma_{\sigma_R}\) between 0 and 10.

Priors.

Priors range from uninformative to very informative or fixed. Priors for compositional logistic parameters are in Table 2 and proportion harvest logistic parameters are in Table 3. Until I figure out how to make a nice table in Rmarkdown, please refer to the attached spreadsheet and comp and harvp tabs.

Unresolved issues and outstanding questions:

1. Reliability of unguided release estimates: These estimates have the least information feeding them and rely on the bias-corrected SWHS release estimates of all rockfish and the trends in release probability evident in the logbook data. The \(\beta4\) term that estimates the guided/unguided effect was given a very informative prior that tied the release probability of private anglers tightly to that of the charter fleet. The model is then trying to balance the three species complex estimates (pelagic, yelloweye and other) so that they sum to the total unguided releases estimated from the bias corrected SWHS data. For the most part this seems reasonable and appears to work, but there are certain areas where the estimates are “wonky”:

   1. Total rockfish releases more or less align with the total releases estimated with the Howard methods. Presumably, much of the discrepancy results from the substantial bias in release estimates from the SWHS. Interestingly, the logbook data indicates that the SWHS underestimates harvests but overestimates releases by a significant factor (Figure 23 and 24 below).
   2. In general, release estimates of black rockfish are substantially lower than those calculated using the Howard methods. Presumably, much of this derives from the bias correction of the SWHS release estimates.
   3. Yelloweye release estimates also differ considerably from the Howard estimates, but unlike black rockfish are sometimes lower and sometimes higher. Two areas in particular are a little head scratching. Yelloweye releases in the Kodiak Northeast area in particular are significantly lower than for guided anglers with the same pattern evident in Cook Inlet to a lesser extent. Cook Inlet yelloweye numbers are very small, so this is a sample size issue with little consequence. The cause of the Kodiak northeast estimates is not clear to me at this point, but the model estimates the proportion harvested by unguided anglers to be much lower than that of guided anglers, even with the informative prior on \(\beta4\). This must be a product of the bias corrected SWHS release estimates and how the model is partitioning that estimate into the 3 species complexes, but itis a bit a of head scratcher.

2. Proportion guided estimates: There is not much data on this proportion prior to 2011 and it is not modeled with any sort of trend as was done for species composition and harvest proportions. With the exception of Cook Inlet and North Gulf Coast areas, there is little, if any, trend apparent in the data and perhaps this approach is the best available given the data available. However, if there are data sources somewhere that could inform this part of the model they could be incorporated.

3. Prior choices in general need to be vetted. The priors on the logistic curves are fairly informed in an effort to achieve the desired shapes for hindcasting. Ideally, sensitivity testing would occur but the model is very slow to converge. The beta parameters on the logistic curves have required a lot of work on the priors to reach convergence.

4. Proportion harvest estimates for non-pelagic, non-yelloweye in Kodiak WKMA: I need to adjust the prior on the inflection point, \(\beta3\), so that it is forced to occur after 2006. Right now the model is estimating inflection in two Kodiak areas before that point where there is no data to justify a shift. The current inflection is a result of the hierachichal model.

5. Proportion pelagic in PWS and CSEO: The parameters for these particular proportions are very slow to converge. For the CSEO, the estimates of the \(\beta\) parameters are similar to the other Southeast areas, but the mixing is poor over the length of the chains. In this case I think they will ultimately converge with a very long model run and the shape of the curve in the model output looks acceptable. For the two PWS areas the model seems to struggle with the disparate proportional data from the logbook and the port sampling. There is some wandering in the chains of the \(\beta0\) and \(\beta1\) terms and spikiness in the \(\beta2\) terms. I’ve been working on constraining the hyperpriors for PWS \(beta2\). Similar to CSEO, it may just entail a very long model run to reach convergence, but the shape of the curves looks reasonable.

Next steps:

Once the model is finalized, harvest and release numbers need to be converted into biomass removals. This is a two step process where release mortality estimates are applied to the release estimates to estimate the number of released rockfish that do not survive. This is based on studies and will reflect the values that the department has been using with the Howard methods. Region 2 (both Southcentral and Kodiak) have release-at-depth estimates from a number of years that they apply across all years and then calculate mortality rates based on those estiates. Southease does not have release-at-depth data and simply applies an assumed rate based on research.

Once release mortality is calculated average weight data is applied to convert numbers to biomass. The plan is to incorporate all of this into the model to propogate uncertainty into the posteriors. However, the model already takes a long time to run and I may explore a simpler approach using the posteriors from the numbers model to speed up processing.

Results

• Model: LB_fit_3pH

• Model Run: Gen3aa_indcomp_swhsR_FULL_thru2023_1e+06_2025-09-11 (Naming convention: modelname_thruYEAR_iters_rundate)

• Proportion of parmaters converged (Rhat <= 1.1): 0.995

• See end of document for summary of unconverged parameters.

Figure X.- Rhat values and proportion of parameters that converged (Rhat < 1.1.)

Estimate comparison

Since previous estimates of rockfish harvest have been produced these first 3 graphs will be used to show how the modeled estimates compare to the estimates produced earlier. For total rockfish the estimates are in general agreement although differences are noted. These estimates should be more reliable because they include both SWHS and guide logbook data, handle variance more appropriately, use hierarchical distributions when data is missing, directly consider observation error and are produced using reproducible research.

Figure 3.- Total rockfish harvests 1996-2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 3.- Total rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Notes from Adam: When looking at only black rockfish the most significant differences are for the Prince William Sound Inside area. I did not spend a great deal of time tracking this down although it looks like the previous version used bad values for \(P_{(black)ayu}\) for at least unguided anglers. For the moment I would ignore the results for BSIA and SOKO2SAP. I think it is possible to give approximate values for these areas but it will require a little more coding which I have yet to do.

Figure 4.- Black rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

And black rockfish releases…

Figure 5.- Black rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- Yellow rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- Yellow rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 8.- DSR rockfish (excluding yelloweye) harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 9.- DSR rockfish releases (including yelloweye) 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 11.- Slope rockfish harvests 1996-2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 12.- Slope rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Total Biomass Removal Estimates

Figure 13.- Black rockfish estimated total removals in lbs in 1996–2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

Figure 14.- Yellow rockfish estimated total removals in lbs in 1996–2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

Figure 15.- Pelagic rockfish estimated total removals in lbs in 1996–2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

Figure 16.- Non-yelloweye, demersal shelf rockfish estimated total removals in lbs in 1996-2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

Figure 17.- Slope rockfish estimated total removals in lbs in 1996-2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

Model fit

Logbook residuals

Figure 18.- Residuals from logbook harvests.

SWHS residuals

Figure 19.- Residuals from SWHS harvests.

Figure 20.- Residual of SWHS releases.

Parameter estimates

P(Charter)

These histograms show the posterior distribution of the mean percent of rockfish harvested by the charter fleet.

Figure 21.- Mean percent of harvest by charter anglers.

When considered annually we see the percent of rockfish harvested by the charter fleet follows our data fairly well although the model smooths out the changes and we just do not have much information about this ratio. Prior to 2011 the percent charter is confounded with SWHS bias and should be mostly discounted.

Figure 22.- Annual estimates of the percent of harvest by charter anglers for 16 commerical fishing manamgent areas, 1996-2023.

P(Harvest)

These plots show the fitted logistic line to the proportion of caught rockfish that are harvested. These estimates are used for hindcasting catch estimates based on the harvest data in early years when catch estimates are unavailable.

Figure 23.- Annual proportion of pelagic rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 24.- Annual proportion of yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 25.- Annual proportion of non-pelagic, non-yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note, that this is not estimated for Southeast areas because non=pelagics are divided between DSR (including yelloweye) and Slope species.

## NULL

## NULL

SWHS bias

Figure 23 shows the mean estimate for SWHS bias in harvests and releases. Cook Inlet, North Gulf Coast and North Southeast Inside all look pretty good while most other areas have substantial bias. Prince William Sound Inside has the largest bias. Bias in release estimates is substantial and whereas the SWHS appears to underestimate harvests, it appears to greatly overestimates releases by a factor of 2 or more in most areas as derived from logbook reported releases.

Figure 28.- Mean SWHS bias for harvests and catches. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.

Our estimates of SWHS harvest bias track observations fairly well when he have guided harvest estimates. The estimates of release bias in the SWHS data track observed patterns to an extent, but appear to smooth these more volatile disagreements with the logbook data. Adam postulated in his initial start on this that some of this could be the result of the estimates of the proportion guided. This value was not modelled with a trend and thus applies a constant estimate when hindcasting. Data on these relationships could greatly improve this model.

Figure 29.- Annual estimates of SWHS bias in harvests and releases for 16 commerical fishing manamgent areas, 1996-2023. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.

P(pelagic)

We model the percentage of pelagic rockfish in the harvest because we have the information for charter anglers (via logbooks) starting in 1998. Other than looking at the model estimates you can use Figure 25 to compare the two data streams for pelagic rockfish harvest. In general they are in agreement with major exceptions in Price William Sound inside, Prince William Sound outside (early in the time series) and South Southeast inside.

Figure 30.- Annual estimates of the percent of the sport harvest that was pelagic rockfish for 16 commerical fishing manamgent areas, 1996-2023.

P(black|pelagic)

Note that in Southeast Alaska we only have composition data starting in 2006. Tania dug up old SE data, but it did not provide any useful data for species apportionment. For the most part, P(black|pelagic) is relatively constant across areas, with the exception of Cook Inlet and NSEI in Southeast AK. It may be worth discussing whether the shifts in those areas is a result of improved or changing species identification rather than actual shift in the species composition of the catch.

Figure 31.- Annual estimates of the percent of the sport harvest of pelagic rockfish that were black rockfish for 16 commerical fishing manamgent areas, 1996-2023. Kodiak panels include data from a hydroacoustic survey and the proportion of pelagic rockfish that are black in those areas (red) and the adjusted proportions based on obseved harvests for charter (blue) and private (cyan) users.

P(yelloweye|non-pelagic / yelloweye|DSR)

Figure 32.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were yelloweye rockfish for 16 commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

P(DSR|non-pelagic)

Figure 33.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were DSR rockfish for 6 Southeast commerical fishing manamgent areas, 1996-2023.

P(slope|non-pelagic)

Figure 34.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

P(slope|non-pelagic & non-yellowye) For release estimates

Figure 35.- Annual estimates of the percent of the sport non-pelagic, non-yelloweye releases that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023.

Weight Fits

Figure 36.- Mean weights of black rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.

Figure 37.- Mean weights of yelloweye rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.

Figure 38.- Mean weights of non-black, pelagic rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.

Figure 39.- Mean weights of non-yelloweye, demersal shelf rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.

Figure 40.- Mean weights of slope rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.

### Summary of unconverged parameters:

Table X. Unconverged parameters.

variable	Freq
beta0_pelagic	3
beta1_pelagic	3
beta2_pelagic	1
beta2_pH	6
H_ay	1
H_ayu	2
Hb_ay	1
Hb_ayg	2
Hb_ayu	1
Ho_ay	3
Ho_ayg	1
Ho_ayu	3
Hp_ay	1
Hp_ayg	2
Hp_ayu	1
Hy_ay	2
Hy_ayg	2
Hy_ayu	2
lambda_H	2
mu_beta2_pH	1
p_dsr	2
R_ay	13
R_ayg	3
R_ayu	13
Rb_ay	14
Rb_ayg	3
Rb_ayu	14
Rd_ay	1
Rd_ayu	1
Ro_ay	15
Ro_ayg	9
Ro_ayu	37
Rp_ay	13
Rp_ayg	3
Rp_ayu	13
Rs_ay	1
Rs_ayu	1
Ry_ay	18
Ry_ayg	3
Ry_ayu	27
tau_beta5_pH	1

area	variable	year	user	species	Rhat
BSAI	Ro_ayg	6			1.276307
BSAI	Ry_ayu	2			1.242258
BSAI	Ry_ay	2			1.242113
BSAI	Ro_ayu	1			1.228472
BSAI	Ro_ayu	19			1.227961
BSAI	Ro_ayu	13			1.227196
BSAI	Ro_ay	1			1.227048
BSAI	Ro_ay	19			1.226696
BSAI	Ro_ay	13			1.226130
BSAI	Rb_ayg	10			1.225284
BSAI	Rp_ayg	10			1.221863
BSAI	R_ayg	10			1.221602
BSAI	Ry_ay	16			1.213913
BSAI	Ry_ayu	16			1.213756
BSAI	Ry_ayu	39			1.203882
BSAI	Ry_ay	39			1.203546
BSAI	Ro_ay	6			1.183249
BSAI	Rb_ayg	11			1.173842
BSAI	Hb_ayu	4			1.171902
BSAI	Hp_ayu	4			1.171153
BSAI	Rp_ayg	11			1.169101
BSAI	Ry_ayu	1			1.169046
BSAI	Ry_ay	1			1.168980
BSAI	R_ayg	11			1.168513
BSAI	Ro_ayu	6			1.165077
BSAI	Hp_ay	4			1.164470
BSAI	Hb_ay	4			1.162322
BSAI	Hy_ay	16			1.161881
BSAI	Hy_ayu	19			1.161558
BSAI	Hy_ayu	16			1.161363
BSAI	Ro_ayg	2			1.159886
BSAI	Hy_ay	19			1.157705
BSAI	Ry_ay	3			1.155741
BSAI	Ry_ayu	3			1.155653
BSAI	Ry_ay	15			1.155407
BSAI	Ry_ayu	15			1.155132
BSAI	Ro_ayu	42			1.154656
BSAI	Ro_ay	42			1.154244
BSAI	Ho_ayg	10			1.152568
BSAI	H_ayu	4			1.152397
BSAI	Ry_ayu	43			1.152270
BSAI	Ry_ay	43			1.151687
BSAI	H_ay	4			1.148473
BSAI	Ro_ayg	4			1.144158
BSAI	Ry_ay	25			1.139140
BSAI	Ry_ayu	25			1.139099
BSAI	Rp_ayu	8			1.136545
BSAI	R_ayu	8			1.135939
BSAI	Hb_ayg	12			1.135020
BSAI	Ry_ayg	19			1.132499
BSAI	Ro_ayu	2			1.131266
BSAI	Ho_ayu	19			1.130762
BSAI	Rb_ayg	4			1.129934
BSAI	R_ayg	4			1.129767
BSAI	Hp_ayg	12			1.129758
BSAI	Rp_ayg	4			1.129479
BSAI	Ro_ay	2			1.126758
BSAI	Ho_ay	19			1.125246
BSAI	Rp_ay	8			1.125095
BSAI	Ho_ayu	14			1.124883
BSAI	R_ay	8			1.124188
BSAI	Ho_ay	14			1.122401
BSAI	Hy_ayg	7			1.122208
BSAI	Rb_ayu	8			1.122204
BSAI	Ho_ayu	3			1.122037
BSAI	Ro_ayu	3			1.121267
BSAI	Ry_ayu	27			1.121129
BSAI	Ry_ay	27			1.121021
BSAI	Ro_ay	3			1.120071
BSAI	Hb_ayg	11			1.119465
BSAI	Ry_ayg	9			1.116914
BSAI	Rb_ayu	4			1.116144
BSAI	Hy_ayg	4			1.115245
BSAI	Ro_ayg	13			1.114436
BSAI	Ry_ayg	21			1.114183
BSAI	Ho_ay	3			1.114048
BSAI	Hp_ayg	11			1.113927
BSAI	Rb_ay	8			1.111148
BSAI	Rb_ay	4			1.110738
CI	Ro_ayg	7			1.130369
CI	Ro_ay	7			1.120050
CSEO	beta2_pH			3	1.235047
EWYKT	Ry_ayu	44			1.236569
EWYKT	Ry_ay	44			1.235413
EWYKT	beta2_pH			3	1.228422
EWYKT	Rd_ayu	44			1.198739
EWYKT	Rd_ay	44			1.180236
EWYKT	Rs_ayu	37			1.133370
EWYKT	p_dsr	45	2		1.125572
EWYKT	p_dsr	46	2		1.123704
EWYKT	Rs_ay	37			1.120068
EWYKT	Ry_ayu	47			1.114626
EWYKT	Ry_ay	47			1.114328
EWYKT	Ry_ayu	26			1.111692
NG	tau_beta5_pH			3	1.131633
NSEI	beta2_pH			3	1.364712
NSEI	beta0_pelagic				1.253654
NSEI	beta1_pelagic				1.209524
NSEO	beta2_pH			3	1.221830
PWSI	mu_beta2_pH			3	1.297944
PWSO	Ro_ayu	9			1.139942
PWSO	beta1_pelagic				1.135034
PWSO	beta0_pelagic				1.118457
SOKO2SAP	Rp_ay	1			1.291124
SOKO2SAP	R_ay	1			1.291124
SOKO2SAP	Rp_ayu	1			1.291124
SOKO2SAP	R_ayu	1			1.291124
SOKO2SAP	Rb_ay	1			1.291121
SOKO2SAP	Rb_ayu	1			1.291121
SOKO2SAP	Rb_ay	5			1.290985
SOKO2SAP	Rb_ayu	5			1.290985
SOKO2SAP	Rp_ay	5			1.290982
SOKO2SAP	R_ay	5			1.290982
SOKO2SAP	Rp_ayu	5			1.290982
SOKO2SAP	R_ayu	5			1.290982
SOKO2SAP	Rp_ay	6			1.290952
SOKO2SAP	R_ay	6			1.290952
SOKO2SAP	Rp_ayu	6			1.290952
SOKO2SAP	R_ayu	6			1.290952
SOKO2SAP	Rb_ay	6			1.290948
SOKO2SAP	Rb_ayu	6			1.290948
SOKO2SAP	R_ay	13			1.290912
SOKO2SAP	R_ayu	13			1.290912
SOKO2SAP	Rp_ay	13			1.290912
SOKO2SAP	Rp_ayu	13			1.290912
SOKO2SAP	Rb_ay	13			1.290911
SOKO2SAP	Rb_ayu	13			1.290911
SOKO2SAP	Rp_ay	10			1.290904
SOKO2SAP	R_ay	10			1.290904
SOKO2SAP	Rp_ayu	10			1.290904
SOKO2SAP	R_ayu	10			1.290904
SOKO2SAP	Rb_ay	10			1.290904
SOKO2SAP	Rb_ayu	10			1.290904
SOKO2SAP	Rp_ay	2			1.290904
SOKO2SAP	R_ay	2			1.290904
SOKO2SAP	Rp_ayu	2			1.290904
SOKO2SAP	R_ayu	2			1.290904
SOKO2SAP	Rb_ay	2			1.290904
SOKO2SAP	Rb_ayu	2			1.290904
SOKO2SAP	Rp_ay	7			1.290904
SOKO2SAP	R_ay	7			1.290904
SOKO2SAP	Rp_ayu	7			1.290904
SOKO2SAP	R_ayu	7			1.290904
SOKO2SAP	Rb_ay	7			1.290904
SOKO2SAP	Rb_ayu	7			1.290904
SOKO2SAP	R_ayu	11			1.290249
SOKO2SAP	Rp_ayu	11			1.290249
SOKO2SAP	R_ay	11			1.290248
SOKO2SAP	Rp_ay	11			1.290248
SOKO2SAP	Rb_ayu	11			1.290233
SOKO2SAP	Rb_ay	11			1.290232
SOKO2SAP	Rb_ayu	4			1.289867
SOKO2SAP	Rb_ay	4			1.289867
SOKO2SAP	Rp_ayu	4			1.289820
SOKO2SAP	R_ayu	4			1.289820
SOKO2SAP	Rp_ay	4			1.289820
SOKO2SAP	R_ay	4			1.289820
SOKO2SAP	Rb_ayu	9			1.285153
SOKO2SAP	Rb_ay	9			1.285153
SOKO2SAP	R_ay	9			1.283855
SOKO2SAP	R_ayu	9			1.283855
SOKO2SAP	Rp_ayu	9			1.283855
SOKO2SAP	Rp_ay	9			1.283855
SOKO2SAP	Rb_ay	8			1.268907
SOKO2SAP	Rb_ayu	8			1.268900
SOKO2SAP	R_ay	8			1.268100
SOKO2SAP	Rp_ay	8			1.268099
SOKO2SAP	R_ayu	8			1.268093
SOKO2SAP	Rp_ayu	8			1.268092
SOKO2SAP	R_ay	3			1.207112
SOKO2SAP	Rp_ay	3			1.207112
SOKO2SAP	R_ayu	3			1.207111
SOKO2SAP	Rp_ayu	3			1.207103
SOKO2SAP	Rb_ay	3			1.206884
SOKO2SAP	Rb_ayu	3			1.206871
SOKO2SAP	Ro_ayu	46			1.191164
SOKO2SAP	Ro_ay	46			1.190746
SOKO2SAP	Ro_ayu	5			1.164844
SOKO2SAP	Ro_ay	5			1.160194
SOKO2SAP	Ry_ayu	13			1.152701
SOKO2SAP	Ry_ay	13			1.152161
SOKO2SAP	Ro_ayu	8			1.130239
SOKO2SAP	Ro_ayu	6			1.128554
SOKO2SAP	Ro_ay	8			1.128193
SOKO2SAP	Ry_ayu	2			1.128131
SOKO2SAP	Ry_ay	2			1.126357
SOKO2SAP	Ro_ay	6			1.125961
SOKO2SAP	Ry_ayu	31			1.124012
SOKO2SAP	Ry_ay	31			1.124002
SOKO2SAP	Ry_ayu	7			1.117956
SOKO2SAP	Ry_ay	7			1.116976
SSEI	beta2_pH			3	1.252131
SSEI	beta0_pelagic				1.213930
SSEI	beta1_pelagic				1.172380
SSEI	lambda_H				1.143752
SSEO	beta2_pelagic				1.410184
SSEO	beta2_pH			3	1.324908
SSEO	H_ayu	1			1.111804
WKMA	Ro_ayu	2			1.229179
WKMA	Ry_ayu	7			1.137817
WKMA	Ry_ayu	32			1.120222
WKMA	Ry_ay	32			1.119388
afognak	Ro_ayu	5			1.142833
afognak	Ro_ayu	20			1.129293
eastside	Ro_ayu	8			1.285699
eastside	Ro_ayu	3			1.283581
eastside	Ro_ayu	6			1.254135
eastside	Ro_ayu	17			1.231237
eastside	Ro_ayu	1			1.228355
eastside	Ro_ayu	4			1.227216
eastside	Ro_ayu	21			1.225243
eastside	Ro_ayu	2			1.223828
eastside	Ro_ayu	23			1.214491
eastside	Ro_ayu	27			1.213858
eastside	Ry_ayu	46			1.211023
eastside	Ro_ayu	7			1.201360
eastside	Ro_ayu	46			1.199784
eastside	Ry_ayu	12			1.194168
eastside	Ry_ayu	13			1.188644
eastside	Ro_ayu	11			1.175616
eastside	Ro_ayu	22			1.172040
eastside	Ry_ayu	41			1.164570
eastside	Ry_ay	41			1.164367
eastside	Ro_ayu	33			1.158951
eastside	Ry_ayu	15			1.152462
eastside	Ro_ayu	9			1.147760
eastside	Ro_ayu	29			1.145237
eastside	Ry_ayu	42			1.144808
eastside	Ry_ayu	1			1.136968
eastside	Ro_ayg	13			1.133173
eastside	Ro_ayu	12			1.131688
eastside	Ro_ay	13			1.129228
eastside	Ro_ayu	25			1.126215
eastside	Ry_ay	42			1.124000
eastside	Ro_ayg	1			1.123669
eastside	Ry_ayu	20			1.123615
eastside	Ro_ayu	45			1.121040
eastside	Ry_ayu	18			1.120972
eastside	Ro_ay	1			1.118670
northeast	Ro_ayu	5			1.150564
northeast	Ro_ayg	10			1.138880
northeast	lambda_H				1.131180
northeast	Ro_ay	10			1.126792
northeast	Ro_ayu	3			1.121046
northeast	Ro_ayg	5			1.120858

Parameter estimates:

Summary Table of Parameter Estimates

Parameter	mean	sd	Lower_CI	Median	Upper_CI
mu_bc_H[1]	-0.095	0.078	-0.235	-0.101	0.075
mu_bc_H[2]	-0.061	0.053	-0.152	-0.065	0.053
mu_bc_H[3]	-0.417	0.070	-0.548	-0.419	-0.276
mu_bc_H[4]	-0.981	0.190	-1.358	-0.977	-0.620
mu_bc_H[5]	0.656	0.722	-0.244	0.543	2.304
mu_bc_H[6]	-2.260	0.305	-2.844	-2.266	-1.663
mu_bc_H[7]	-0.472	0.108	-0.691	-0.473	-0.267
mu_bc_H[8]	0.220	0.349	-0.378	0.192	0.979
mu_bc_H[9]	-0.283	0.135	-0.547	-0.287	0.000
mu_bc_H[10]	-0.088	0.068	-0.217	-0.089	0.051
mu_bc_H[11]	-0.139	0.038	-0.214	-0.139	-0.064
mu_bc_H[12]	-0.258	0.103	-0.475	-0.255	-0.063
mu_bc_H[13]	-0.109	0.072	-0.248	-0.112	0.032
mu_bc_H[14]	-0.291	0.092	-0.472	-0.288	-0.118
mu_bc_H[15]	-0.339	0.047	-0.431	-0.338	-0.243
mu_bc_H[16]	-0.369	0.366	-1.011	-0.392	0.433
mu_bc_R[1]	1.234	0.110	1.017	1.235	1.456
mu_bc_R[2]	1.361	0.089	1.175	1.365	1.518
mu_bc_R[3]	1.256	0.094	1.071	1.254	1.440
mu_bc_R[4]	0.896	0.183	0.494	0.903	1.229
mu_bc_R[5]	1.307	0.364	0.584	1.292	2.042
mu_bc_R[6]	-1.346	0.348	-2.017	-1.354	-0.658
mu_bc_R[7]	0.538	0.183	0.170	0.539	0.901
mu_bc_R[8]	0.612	0.147	0.333	0.613	0.906
mu_bc_R[9]	0.306	0.197	-0.115	0.318	0.658
mu_bc_R[10]	1.171	0.112	0.944	1.173	1.389
mu_bc_R[11]	1.152	0.068	1.024	1.152	1.288
mu_bc_R[12]	0.870	0.165	0.543	0.874	1.186
mu_bc_R[13]	0.922	0.082	0.757	0.923	1.079
mu_bc_R[14]	0.910	0.123	0.661	0.912	1.148
mu_bc_R[15]	0.716	0.082	0.552	0.716	0.879
mu_bc_R[16]	1.166	0.104	0.960	1.164	1.372
tau_pH[1]	6.338	0.548	5.332	6.325	7.490
tau_pH[2]	1.870	0.209	1.485	1.866	2.278
tau_pH[3]	2.204	0.232	1.775	2.197	2.695
beta0_pH[1,1]	0.541	0.164	0.180	0.552	0.835
beta0_pH[2,1]	1.466	0.143	1.168	1.471	1.730
beta0_pH[3,1]	1.392	0.186	0.978	1.408	1.706
beta0_pH[4,1]	1.569	0.198	1.136	1.584	1.915
beta0_pH[5,1]	-0.903	0.243	-1.444	-0.889	-0.477
beta0_pH[6,1]	-0.466	0.383	-1.293	-0.391	-0.024
beta0_pH[7,1]	0.737	0.088	0.567	0.738	0.907
beta0_pH[8,1]	-0.700	0.249	-1.228	-0.687	-0.271
beta0_pH[9,1]	-0.616	0.247	-1.143	-0.605	-0.173
beta0_pH[10,1]	0.344	0.162	0.001	0.347	0.648
beta0_pH[11,1]	-0.117	0.152	-0.425	-0.114	0.171
beta0_pH[12,1]	0.495	0.162	0.174	0.494	0.793
beta0_pH[13,1]	0.002	0.130	-0.258	0.003	0.261
beta0_pH[14,1]	-0.249	0.145	-0.543	-0.246	0.031
beta0_pH[15,1]	-0.050	0.147	-0.344	-0.052	0.238
beta0_pH[16,1]	-0.254	0.170	-0.623	-0.244	0.051
beta0_pH[1,2]	2.597	0.218	2.162	2.597	3.001
beta0_pH[2,2]	2.871	0.165	2.549	2.869	3.211
beta0_pH[3,2]	3.392	0.184	3.037	3.387	3.763
beta0_pH[4,2]	3.087	0.160	2.783	3.086	3.403
beta0_pH[5,2]	4.459	1.328	2.653	4.203	7.953
beta0_pH[6,2]	3.281	0.245	2.809	3.276	3.763
beta0_pH[7,2]	1.921	0.239	1.447	1.926	2.379
beta0_pH[8,2]	2.825	0.206	2.428	2.827	3.232
beta0_pH[9,2]	3.882	0.276	3.345	3.885	4.428
beta0_pH[10,2]	3.796	0.233	3.360	3.790	4.259
beta0_pH[11,2]	1.857	0.167	1.526	1.861	2.181
beta0_pH[12,2]	1.621	0.199	1.232	1.622	2.017
beta0_pH[13,2]	2.342	0.202	1.948	2.341	2.731
beta0_pH[14,2]	1.627	0.179	1.287	1.625	1.988
beta0_pH[15,2]	2.403	0.197	2.016	2.405	2.782
beta0_pH[16,2]	2.517	0.206	2.122	2.518	2.911
beta0_pH[1,3]	0.435	0.585	-0.978	0.509	1.286
beta0_pH[2,3]	2.072	0.181	1.713	2.078	2.422
beta0_pH[3,3]	2.658	0.162	2.354	2.654	2.978
beta0_pH[4,3]	3.009	0.182	2.649	3.006	3.368
beta0_pH[5,3]	3.065	1.798	0.731	2.690	7.659
beta0_pH[6,3]	1.166	0.379	0.485	1.149	1.986
beta0_pH[7,3]	0.568	0.196	0.194	0.568	0.964
beta0_pH[8,3]	0.280	0.194	-0.097	0.282	0.660
beta0_pH[9,3]	-1.693	0.966	-3.539	-1.686	-0.249
beta0_pH[10,3]	-0.316	0.661	-1.716	-0.316	0.844
beta0_pH[11,3]	1.088	0.468	-0.013	1.111	1.989
beta0_pH[12,3]	0.775	0.477	-0.334	0.818	1.542
beta0_pH[13,3]	1.082	0.458	-0.049	1.201	1.685
beta0_pH[14,3]	0.620	0.496	-0.524	0.667	1.449
beta0_pH[15,3]	0.959	0.356	0.165	1.047	1.441
beta0_pH[16,3]	1.034	0.381	0.082	1.137	1.541
beta1_pH[1,1]	3.184	0.634	2.299	3.057	4.841
beta1_pH[2,1]	1.742	0.240	1.314	1.726	2.269
beta1_pH[3,1]	1.905	0.356	1.403	1.854	2.827
beta1_pH[4,1]	2.119	0.348	1.567	2.080	2.937
beta1_pH[5,1]	2.222	0.282	1.727	2.203	2.828
beta1_pH[6,1]	2.467	0.739	1.422	2.333	4.338
beta1_pH[7,1]	0.000	0.000	0.000	0.000	0.000
beta1_pH[8,1]	2.695	0.660	1.773	2.568	4.434
beta1_pH[9,1]	2.182	0.322	1.620	2.162	2.921
beta1_pH[10,1]	2.150	0.279	1.698	2.136	2.677
beta1_pH[11,1]	3.342	0.197	2.980	3.335	3.744
beta1_pH[12,1]	2.890	0.197	2.510	2.884	3.282
beta1_pH[13,1]	2.705	0.197	2.320	2.698	3.106
beta1_pH[14,1]	3.329	0.208	2.943	3.323	3.754
beta1_pH[15,1]	2.639	0.206	2.263	2.635	3.060
beta1_pH[16,1]	3.068	0.223	2.656	3.055	3.541
beta1_pH[1,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[2,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[3,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[4,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[5,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[6,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[7,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[8,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[9,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[10,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[11,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[12,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[13,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[14,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[15,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[16,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[1,3]	2.833	1.395	1.199	2.397	6.497
beta1_pH[2,3]	0.000	0.000	0.000	0.000	0.000
beta1_pH[3,3]	0.000	0.000	0.000	0.000	0.000
beta1_pH[4,3]	0.000	0.000	0.000	0.000	0.000
beta1_pH[5,3]	0.000	0.000	0.000	0.000	0.000
beta1_pH[6,3]	0.000	0.000	0.000	0.000	0.000
beta1_pH[7,3]	0.000	0.000	0.000	0.000	0.000
beta1_pH[8,3]	3.516	0.664	2.217	3.507	4.853
beta1_pH[9,3]	3.921	1.155	2.234	3.829	6.343
beta1_pH[10,3]	5.182	1.918	2.670	4.832	10.041
beta1_pH[11,3]	1.544	0.518	0.474	1.529	2.630
beta1_pH[12,3]	2.532	0.538	1.613	2.493	3.758
beta1_pH[13,3]	0.471	0.498	0.000	0.299	1.710
beta1_pH[14,3]	1.628	0.561	0.574	1.599	2.805
beta1_pH[15,3]	0.361	0.389	0.000	0.212	1.281
beta1_pH[16,3]	0.357	0.411	0.000	0.180	1.431
beta2_pH[1,1]	0.446	0.145	0.235	0.425	0.799
beta2_pH[2,1]	0.899	0.536	0.332	0.769	2.350
beta2_pH[3,1]	0.834	0.682	0.215	0.661	2.480
beta2_pH[4,1]	0.604	0.294	0.243	0.545	1.344
beta2_pH[5,1]	1.943	1.122	0.475	1.733	4.727
beta2_pH[6,1]	0.365	0.378	0.123	0.267	1.429
beta2_pH[7,1]	0.000	0.000	0.000	0.000	0.000
beta2_pH[8,1]	0.290	0.135	0.140	0.268	0.558
beta2_pH[9,1]	0.516	0.235	0.233	0.467	1.098
beta2_pH[10,1]	0.728	0.369	0.344	0.650	1.604
beta2_pH[11,1]	0.756	0.171	0.488	0.734	1.143
beta2_pH[12,1]	1.153	0.367	0.720	1.080	2.073
beta2_pH[13,1]	0.841	0.212	0.506	0.814	1.334
beta2_pH[14,1]	0.839	0.176	0.559	0.817	1.236
beta2_pH[15,1]	0.767	0.210	0.411	0.748	1.238
beta2_pH[16,1]	0.776	0.198	0.458	0.760	1.205
beta2_pH[1,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[2,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[3,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[4,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[5,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[6,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[7,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[8,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[9,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[10,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[11,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[12,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[13,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[14,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[15,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[16,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[1,3]	4.115	5.414	0.135	1.043	18.285
beta2_pH[2,3]	0.000	0.000	0.000	0.000	0.000
beta2_pH[3,3]	0.000	0.000	0.000	0.000	0.000
beta2_pH[4,3]	0.000	0.000	0.000	0.000	0.000
beta2_pH[5,3]	0.000	0.000	0.000	0.000	0.000
beta2_pH[6,3]	0.000	0.000	0.000	0.000	0.000
beta2_pH[7,3]	0.000	0.000	0.000	0.000	0.000
beta2_pH[8,3]	6.055	3.996	1.171	5.206	16.461
beta2_pH[9,3]	2.633	4.268	0.220	0.569	15.498
beta2_pH[10,3]	1.926	4.134	0.175	0.427	16.368
beta2_pH[11,3]	-5.185	4.840	-19.253	-3.456	-0.505
beta2_pH[12,3]	-5.248	4.642	-18.720	-3.477	-0.978
beta2_pH[13,3]	-4.912	4.932	-18.914	-2.975	-0.112
beta2_pH[14,3]	-5.409	4.694	-19.082	-3.744	-0.827
beta2_pH[15,3]	-5.209	4.876	-18.865	-3.532	-0.110
beta2_pH[16,3]	-4.896	4.997	-19.535	-3.141	-0.064
beta3_pH[1,1]	36.164	1.304	34.128	35.987	39.519
beta3_pH[2,1]	32.721	0.925	31.079	32.653	34.772
beta3_pH[3,1]	33.229	1.069	31.364	33.181	35.565
beta3_pH[4,1]	33.040	1.067	31.034	33.004	35.233
beta3_pH[5,1]	27.295	0.501	26.446	27.266	28.176
beta3_pH[6,1]	35.303	2.815	30.366	35.129	40.888
beta3_pH[7,1]	25.000	0.000	25.000	25.000	25.000
beta3_pH[8,1]	36.156	2.493	31.258	36.178	41.029
beta3_pH[9,1]	30.240	1.312	27.897	30.147	32.993
beta3_pH[10,1]	32.695	0.904	31.115	32.651	34.432
beta3_pH[11,1]	30.403	0.450	29.513	30.401	31.304
beta3_pH[12,1]	30.454	0.353	29.757	30.457	31.134
beta3_pH[13,1]	32.803	0.536	31.754	32.797	33.869
beta3_pH[14,1]	32.087	0.429	31.291	32.073	32.951
beta3_pH[15,1]	31.316	0.552	30.228	31.313	32.390
beta3_pH[16,1]	30.795	0.481	29.788	30.811	31.730
beta3_pH[1,2]	33.606	4.931	25.508	33.696	41.549
beta3_pH[2,2]	33.582	4.894	25.431	33.742	41.637
beta3_pH[3,2]	30.142	6.999	18.631	30.257	41.393
beta3_pH[4,2]	30.228	6.864	18.729	30.113	41.409
beta3_pH[5,2]	30.168	6.965	18.577	30.262	41.389
beta3_pH[6,2]	29.966	6.989	18.507	29.997	41.325
beta3_pH[7,2]	25.000	0.000	25.000	25.000	25.000
beta3_pH[8,2]	25.000	0.000	25.000	25.000	25.000
beta3_pH[9,2]	25.000	0.000	25.000	25.000	25.000
beta3_pH[10,2]	25.000	0.000	25.000	25.000	25.000
beta3_pH[11,2]	24.000	0.000	24.000	24.000	24.000
beta3_pH[12,2]	24.000	0.000	24.000	24.000	24.000
beta3_pH[13,2]	24.000	0.000	24.000	24.000	24.000
beta3_pH[14,2]	24.000	0.000	24.000	24.000	24.000
beta3_pH[15,2]	24.000	0.000	24.000	24.000	24.000
beta3_pH[16,2]	24.000	0.000	24.000	24.000	24.000
beta3_pH[1,3]	37.142	2.736	32.334	37.017	41.470
beta3_pH[2,3]	33.645	4.918	25.536	33.704	41.614
beta3_pH[3,3]	30.117	6.806	18.530	30.308	41.294
beta3_pH[4,3]	30.172	6.904	18.693	30.250	41.464
beta3_pH[5,3]	25.000	0.000	25.000	25.000	25.000
beta3_pH[6,3]	25.000	0.000	25.000	25.000	25.000
beta3_pH[7,3]	25.000	0.000	25.000	25.000	25.000
beta3_pH[8,3]	41.558	0.241	41.103	41.577	41.944
beta3_pH[9,3]	31.708	1.778	28.444	31.769	34.169
beta3_pH[10,3]	36.247	1.730	33.365	36.016	40.633
beta3_pH[11,3]	40.108	1.496	37.615	40.177	42.268
beta3_pH[12,3]	40.889	0.595	39.630	40.973	41.893
beta3_pH[13,3]	39.691	3.462	30.210	41.078	42.899
beta3_pH[14,3]	40.393	1.025	38.538	40.486	41.926
beta3_pH[15,3]	38.919	3.687	29.818	40.481	42.838
beta3_pH[16,3]	38.777	3.780	29.752	40.193	42.888
beta4_pH[1,1]	0.686	0.287	0.306	0.636	1.288
beta4_pH[2,1]	0.851	0.219	0.543	0.818	1.264
beta4_pH[3,1]	0.885	0.212	0.530	0.857	1.399
beta4_pH[4,1]	0.800	0.269	0.429	0.760	1.339
beta4_pH[5,1]	0.657	0.546	0.084	0.484	2.000
beta4_pH[6,1]	1.838	1.616	0.242	1.330	6.465
beta4_pH[7,1]	1.101	0.626	0.345	0.923	2.462
beta4_pH[8,1]	0.761	0.428	0.226	0.669	1.734
beta4_pH[9,1]	0.921	0.535	0.274	0.787	2.184
beta4_pH[10,1]	0.724	0.276	0.346	0.675	1.280
beta4_pH[11,1]	0.698	0.245	0.354	0.661	1.183
beta4_pH[12,1]	0.925	0.374	0.437	0.844	1.728
beta4_pH[13,1]	0.753	0.270	0.381	0.711	1.288
beta4_pH[14,1]	1.023	0.333	0.562	0.963	1.685
beta4_pH[15,1]	0.920	0.269	0.539	0.874	1.444
beta4_pH[16,1]	0.895	0.354	0.419	0.823	1.644
beta4_pH[1,2]	0.694	0.284	0.306	0.648	1.280
beta4_pH[2,2]	0.851	0.215	0.544	0.819	1.260
beta4_pH[3,2]	0.890	0.211	0.531	0.864	1.404
beta4_pH[4,2]	0.806	0.271	0.432	0.760	1.342
beta4_pH[5,2]	0.668	0.544	0.085	0.496	1.995
beta4_pH[6,2]	1.863	1.618	0.235	1.379	6.554
beta4_pH[7,2]	1.076	0.595	0.354	0.932	2.462
beta4_pH[8,2]	0.766	0.426	0.227	0.671	1.732
beta4_pH[9,2]	0.931	0.534	0.275	0.789	2.159
beta4_pH[10,2]	0.726	0.279	0.346	0.671	1.293
beta4_pH[11,2]	0.699	0.250	0.353	0.651	1.197
beta4_pH[12,2]	0.925	0.374	0.436	0.847	1.721
beta4_pH[13,2]	0.751	0.266	0.379	0.704	1.295
beta4_pH[14,2]	1.022	0.333	0.563	0.969	1.697
beta4_pH[15,2]	0.932	0.266	0.543	0.902	1.452
beta4_pH[16,2]	0.901	0.360	0.419	0.827	1.650
beta4_pH[1,3]	0.688	0.281	0.307	0.642	1.283
beta4_pH[2,3]	0.856	0.217	0.543	0.829	1.261
beta4_pH[3,3]	0.884	0.214	0.532	0.859	1.411
beta4_pH[4,3]	0.803	0.269	0.430	0.759	1.347
beta4_pH[5,3]	0.665	0.549	0.084	0.488	1.987
beta4_pH[6,3]	1.888	1.605	0.239	1.413	6.481
beta4_pH[7,3]	1.098	0.609	0.348	0.947	2.490
beta4_pH[8,3]	0.771	0.431	0.228	0.677	1.735
beta4_pH[9,3]	0.914	0.535	0.273	0.777	2.157
beta4_pH[10,3]	0.724	0.276	0.345	0.677	1.291
beta4_pH[11,3]	0.688	0.244	0.353	0.644	1.191
beta4_pH[12,3]	0.917	0.370	0.440	0.834	1.719
beta4_pH[13,3]	0.743	0.264	0.380	0.698	1.287
beta4_pH[14,3]	1.028	0.332	0.563	0.970	1.693
beta4_pH[15,3]	0.918	0.267	0.537	0.875	1.433
beta4_pH[16,3]	0.899	0.365	0.417	0.820	1.661
beta4_pH[1,4]	0.698	0.284	0.309	0.655	1.289
beta4_pH[2,4]	0.847	0.217	0.540	0.818	1.263
beta4_pH[3,4]	0.880	0.212	0.531	0.855	1.401
beta4_pH[4,4]	0.807	0.268	0.430	0.769	1.343
beta4_pH[5,4]	0.662	0.536	0.084	0.503	1.964
beta4_pH[6,4]	1.818	1.584	0.233	1.323	6.410
beta4_pH[7,4]	1.103	0.600	0.347	0.954	2.493
beta4_pH[8,4]	0.761	0.432	0.227	0.665	1.733
beta4_pH[9,4]	0.931	0.546	0.274	0.781	2.181
beta4_pH[10,4]	0.720	0.272	0.344	0.666	1.293
beta4_pH[11,4]	0.685	0.246	0.353	0.645	1.191
beta4_pH[12,4]	0.924	0.380	0.436	0.830	1.729
beta4_pH[13,4]	0.742	0.264	0.379	0.695	1.289
beta4_pH[14,4]	1.009	0.329	0.559	0.953	1.696
beta4_pH[15,4]	0.913	0.267	0.535	0.875	1.447
beta4_pH[16,4]	0.899	0.365	0.419	0.823	1.660
beta4_pH[1,5]	0.691	0.283	0.305	0.639	1.280
beta4_pH[2,5]	0.851	0.214	0.544	0.821	1.262
beta4_pH[3,5]	0.889	0.215	0.535	0.857	1.419
beta4_pH[4,5]	0.811	0.273	0.430	0.773	1.344
beta4_pH[5,5]	0.654	0.544	0.083	0.468	1.992
beta4_pH[6,5]	1.857	1.591	0.245	1.392	6.479
beta4_pH[7,5]	1.110	0.609	0.352	0.967	2.482
beta4_pH[8,5]	0.765	0.432	0.226	0.673	1.735
beta4_pH[9,5]	0.931	0.538	0.278	0.793	2.186
beta4_pH[10,5]	0.728	0.281	0.345	0.676	1.299
beta4_pH[11,5]	0.691	0.243	0.352	0.654	1.189
beta4_pH[12,5]	0.928	0.379	0.435	0.848	1.701
beta4_pH[13,5]	0.744	0.266	0.382	0.696	1.283
beta4_pH[14,5]	1.021	0.333	0.560	0.959	1.696
beta4_pH[15,5]	0.908	0.265	0.538	0.866	1.442
beta4_pH[16,5]	0.897	0.357	0.425	0.818	1.642
beta4_pH[1,6]	0.699	0.284	0.305	0.660	1.283
beta4_pH[2,6]	0.853	0.215	0.544	0.822	1.263
beta4_pH[3,6]	0.885	0.215	0.531	0.859	1.413
beta4_pH[4,6]	0.802	0.264	0.432	0.754	1.348
beta4_pH[5,6]	0.661	0.548	0.084	0.488	1.993
beta4_pH[6,6]	1.840	1.573	0.235	1.365	6.317
beta4_pH[7,6]	1.096	0.617	0.346	0.942	2.473
beta4_pH[8,6]	0.756	0.432	0.225	0.656	1.733
beta4_pH[9,6]	0.922	0.547	0.278	0.769	2.190
beta4_pH[10,6]	0.721	0.276	0.347	0.668	1.278
beta4_pH[11,6]	0.690	0.244	0.352	0.649	1.190
beta4_pH[12,6]	0.925	0.380	0.437	0.840	1.729
beta4_pH[13,6]	0.748	0.262	0.383	0.700	1.287
beta4_pH[14,6]	1.021	0.333	0.561	0.967	1.691
beta4_pH[15,6]	0.915	0.264	0.536	0.875	1.440
beta4_pH[16,6]	0.889	0.355	0.419	0.822	1.644
beta4_pH[1,7]	0.697	0.284	0.306	0.652	1.272
beta4_pH[2,7]	0.851	0.212	0.546	0.821	1.255
beta4_pH[3,7]	0.881	0.206	0.543	0.852	1.388
beta4_pH[4,7]	0.801	0.269	0.433	0.749	1.340
beta4_pH[5,7]	0.646	0.530	0.083	0.491	1.981
beta4_pH[6,7]	1.921	1.632	0.240	1.422	6.514
beta4_pH[7,7]	1.090	0.603	0.347	0.937	2.475
beta4_pH[8,7]	0.764	0.433	0.227	0.669	1.723
beta4_pH[9,7]	0.905	0.536	0.276	0.762	2.179
beta4_pH[10,7]	0.719	0.276	0.346	0.671	1.288
beta4_pH[11,7]	0.693	0.246	0.354	0.651	1.189
beta4_pH[12,7]	0.941	0.382	0.436	0.860	1.736
beta4_pH[13,7]	0.754	0.269	0.379	0.714	1.294
beta4_pH[14,7]	1.034	0.332	0.565	0.992	1.698
beta4_pH[15,7]	0.925	0.264	0.540	0.894	1.439
beta4_pH[16,7]	0.894	0.359	0.422	0.824	1.658
beta4_pH[1,8]	0.690	0.283	0.306	0.641	1.276
beta4_pH[2,8]	0.854	0.216	0.545	0.824	1.262
beta4_pH[3,8]	0.884	0.214	0.538	0.854	1.425
beta4_pH[4,8]	0.810	0.270	0.432	0.770	1.343
beta4_pH[5,8]	0.650	0.524	0.088	0.493	1.962
beta4_pH[6,8]	1.894	1.616	0.240	1.390	6.481
beta4_pH[7,8]	1.098	0.612	0.345	0.944	2.484
beta4_pH[8,8]	0.767	0.423	0.228	0.668	1.720
beta4_pH[9,8]	0.921	0.535	0.276	0.779	2.169
beta4_pH[10,8]	0.728	0.279	0.344	0.689	1.285
beta4_pH[11,8]	0.694	0.247	0.354	0.653	1.186
beta4_pH[12,8]	0.937	0.375	0.440	0.849	1.724
beta4_pH[13,8]	0.748	0.265	0.379	0.703	1.291
beta4_pH[14,8]	1.034	0.336	0.561	0.984	1.701
beta4_pH[15,8]	0.911	0.265	0.537	0.871	1.435
beta4_pH[16,8]	0.906	0.357	0.419	0.839	1.635
beta4_pH[1,9]	0.691	0.283	0.307	0.638	1.282
beta4_pH[2,9]	0.863	0.217	0.545	0.838	1.265
beta4_pH[3,9]	0.881	0.213	0.527	0.858	1.411
beta4_pH[4,9]	0.805	0.271	0.429	0.760	1.335
beta4_pH[5,9]	0.654	0.533	0.085	0.487	1.972
beta4_pH[6,9]	1.820	1.564	0.239	1.356	6.418
beta4_pH[7,9]	1.090	0.609	0.347	0.927	2.484
beta4_pH[8,9]	0.768	0.437	0.227	0.667	1.738
beta4_pH[9,9]	0.914	0.534	0.276	0.777	2.186
beta4_pH[10,9]	0.724	0.275	0.344	0.681	1.286
beta4_pH[11,9]	0.686	0.243	0.351	0.646	1.192
beta4_pH[12,9]	0.937	0.376	0.437	0.847	1.739
beta4_pH[13,9]	0.745	0.271	0.380	0.695	1.295
beta4_pH[14,9]	1.022	0.336	0.560	0.965	1.692
beta4_pH[15,9]	0.914	0.265	0.536	0.874	1.446
beta4_pH[16,9]	0.894	0.364	0.418	0.811	1.647
beta4_pH[1,10]	0.695	0.285	0.308	0.643	1.281
beta4_pH[2,10]	0.847	0.215	0.546	0.815	1.263
beta4_pH[3,10]	0.886	0.210	0.531	0.865	1.415
beta4_pH[4,10]	0.803	0.272	0.430	0.754	1.342
beta4_pH[5,10]	0.676	0.553	0.085	0.505	2.029
beta4_pH[6,10]	1.844	1.591	0.238	1.381	6.437
beta4_pH[7,10]	1.108	0.613	0.349	0.956	2.499
beta4_pH[8,10]	0.763	0.432	0.226	0.663	1.744
beta4_pH[9,10]	0.928	0.539	0.277	0.780	2.202
beta4_pH[10,10]	0.737	0.279	0.347	0.693	1.297
beta4_pH[11,10]	0.690	0.246	0.353	0.646	1.194
beta4_pH[12,10]	0.933	0.380	0.433	0.843	1.714
beta4_pH[13,10]	0.749	0.269	0.381	0.699	1.301
beta4_pH[14,10]	1.028	0.335	0.561	0.974	1.683
beta4_pH[15,10]	0.920	0.268	0.540	0.879	1.448
beta4_pH[16,10]	0.895	0.358	0.421	0.816	1.656
beta4_pH[1,11]	0.685	0.282	0.304	0.633	1.274
beta4_pH[2,11]	0.850	0.212	0.544	0.821	1.264
beta4_pH[3,11]	0.891	0.214	0.528	0.860	1.426
beta4_pH[4,11]	0.799	0.269	0.432	0.751	1.340
beta4_pH[5,11]	0.653	0.531	0.082	0.489	1.982
beta4_pH[6,11]	1.898	1.669	0.242	1.363	6.691
beta4_pH[7,11]	1.087	0.608	0.349	0.941	2.487
beta4_pH[8,11]	0.762	0.430	0.225	0.665	1.730
beta4_pH[9,11]	0.944	0.549	0.276	0.804	2.190
beta4_pH[10,11]	0.735	0.279	0.345	0.689	1.298
beta4_pH[11,11]	0.692	0.246	0.352	0.652	1.193
beta4_pH[12,11]	0.934	0.376	0.440	0.848	1.710
beta4_pH[13,11]	0.745	0.265	0.381	0.693	1.280
beta4_pH[14,11]	1.029	0.338	0.560	0.971	1.693
beta4_pH[15,11]	0.915	0.264	0.537	0.878	1.443
beta4_pH[16,11]	0.897	0.356	0.420	0.821	1.649
beta4_pH[1,12]	0.692	0.277	0.308	0.648	1.281
beta4_pH[2,12]	0.859	0.215	0.542	0.838	1.258
beta4_pH[3,12]	0.888	0.217	0.532	0.856	1.423
beta4_pH[4,12]	0.805	0.267	0.432	0.763	1.338
beta4_pH[5,12]	0.639	0.530	0.084	0.471	1.969
beta4_pH[6,12]	1.849	1.584	0.230	1.383	6.422
beta4_pH[7,12]	1.088	0.609	0.346	0.926	2.467
beta4_pH[8,12]	0.771	0.428	0.228	0.677	1.725
beta4_pH[9,12]	0.928	0.542	0.273	0.789	2.213
beta4_pH[10,12]	0.732	0.278	0.347	0.695	1.290
beta4_pH[11,12]	0.684	0.245	0.349	0.640	1.191
beta4_pH[12,12]	0.937	0.377	0.440	0.855	1.724
beta4_pH[13,12]	0.742	0.262	0.383	0.698	1.283
beta4_pH[14,12]	1.024	0.337	0.561	0.961	1.710
beta4_pH[15,12]	0.917	0.268	0.536	0.877	1.447
beta4_pH[16,12]	0.902	0.367	0.422	0.822	1.664
beta4_pH[1,13]	0.691	0.287	0.307	0.638	1.284
beta4_pH[2,13]	0.856	0.221	0.543	0.824	1.266
beta4_pH[3,13]	0.884	0.212	0.540	0.859	1.405
beta4_pH[4,13]	0.806	0.276	0.430	0.753	1.355
beta4_pH[5,13]	0.658	0.537	0.084	0.497	1.964
beta4_pH[6,13]	1.819	1.521	0.233	1.382	6.270
beta4_pH[7,13]	1.093	0.608	0.347	0.943	2.476
beta4_pH[8,13]	0.764	0.431	0.225	0.663	1.709
beta4_pH[9,13]	0.933	0.545	0.274	0.787	2.187
beta4_pH[10,13]	0.733	0.280	0.347	0.690	1.294
beta4_pH[11,13]	0.693	0.248	0.352	0.654	1.193
beta4_pH[12,13]	0.930	0.380	0.436	0.847	1.724
beta4_pH[13,13]	0.763	0.271	0.379	0.721	1.293
beta4_pH[14,13]	1.028	0.336	0.560	0.978	1.693
beta4_pH[15,13]	0.917	0.269	0.539	0.874	1.442
beta4_pH[16,13]	0.900	0.363	0.420	0.824	1.644
beta4_pH[1,14]	0.702	0.291	0.307	0.654	1.298
beta4_pH[2,14]	0.895	0.214	0.547	0.882	1.271
beta4_pH[3,14]	0.813	0.173	0.525	0.804	1.250
beta4_pH[4,14]	0.825	0.272	0.431	0.785	1.351
beta4_pH[5,14]	0.639	0.528	0.084	0.473	1.952
beta4_pH[6,14]	1.918	1.613	0.237	1.419	6.427
beta4_pH[7,14]	1.097	0.606	0.347	0.943	2.476
beta4_pH[8,14]	0.743	0.421	0.227	0.651	1.693
beta4_pH[9,14]	0.884	0.526	0.271	0.745	2.152
beta4_pH[10,14]	0.742	0.282	0.348	0.696	1.301
beta4_pH[11,14]	0.687	0.249	0.352	0.645	1.192
beta4_pH[12,14]	0.938	0.377	0.440	0.861	1.730
beta4_pH[13,14]	0.763	0.271	0.383	0.715	1.296
beta4_pH[14,14]	1.022	0.328	0.560	0.968	1.688
beta4_pH[15,14]	0.894	0.263	0.534	0.850	1.438
beta4_pH[16,14]	0.905	0.359	0.421	0.844	1.646
beta4_pH[1,15]	0.750	0.294	0.311	0.720	1.296
beta4_pH[2,15]	0.936	0.214	0.560	0.951	1.269
beta4_pH[3,15]	0.964	0.214	0.599	0.929	1.457
beta4_pH[4,15]	0.832	0.271	0.434	0.795	1.352
beta4_pH[5,15]	0.612	0.509	0.083	0.454	1.929
beta4_pH[6,15]	1.800	1.501	0.233	1.362	5.962
beta4_pH[7,15]	1.125	0.616	0.352	0.978	2.510
beta4_pH[8,15]	0.756	0.422	0.227	0.668	1.719
beta4_pH[9,15]	0.891	0.517	0.276	0.756	2.135
beta4_pH[10,15]	0.744	0.280	0.347	0.708	1.296
beta4_pH[11,15]	0.712	0.247	0.356	0.675	1.200
beta4_pH[12,15]	0.942	0.374	0.437	0.867	1.725
beta4_pH[13,15]	0.830	0.276	0.386	0.818	1.313
beta4_pH[14,15]	1.037	0.336	0.560	0.990	1.701
beta4_pH[15,15]	0.985	0.272	0.552	0.965	1.457
beta4_pH[16,15]	0.898	0.357	0.423	0.831	1.656
beta4_pH[1,16]	0.695	0.285	0.306	0.646	1.284
beta4_pH[2,16]	0.918	0.215	0.550	0.918	1.272
beta4_pH[3,16]	0.936	0.212	0.575	0.901	1.456
beta4_pH[4,16]	0.824	0.272	0.435	0.788	1.346
beta4_pH[5,16]	0.616	0.514	0.083	0.446	1.954
beta4_pH[6,16]	1.705	1.412	0.239	1.349	6.008
beta4_pH[7,16]	1.116	0.618	0.350	0.956	2.511
beta4_pH[8,16]	0.774	0.433	0.227	0.683	1.736
beta4_pH[9,16]	0.864	0.511	0.272	0.729	2.100
beta4_pH[10,16]	0.748	0.285	0.346	0.710	1.301
beta4_pH[11,16]	0.677	0.242	0.353	0.634	1.183
beta4_pH[12,16]	0.931	0.374	0.438	0.849	1.716
beta4_pH[13,16]	0.761	0.267	0.384	0.723	1.285
beta4_pH[14,16]	1.023	0.340	0.560	0.965	1.711
beta4_pH[15,16]	0.898	0.255	0.540	0.855	1.432
beta4_pH[16,16]	0.910	0.362	0.422	0.838	1.661
beta4_pH[1,17]	0.683	0.279	0.305	0.633	1.269
beta4_pH[2,17]	0.890	0.211	0.551	0.880	1.266
beta4_pH[3,17]	0.937	0.208	0.568	0.905	1.441
beta4_pH[4,17]	0.824	0.268	0.433	0.797	1.343
beta4_pH[5,17]	0.601	0.503	0.083	0.446	1.881
beta4_pH[6,17]	2.205	1.775	0.245	1.602	6.747
beta4_pH[7,17]	1.171	0.637	0.348	1.029	2.522
beta4_pH[8,17]	0.768	0.434	0.223	0.679	1.732
beta4_pH[9,17]	0.878	0.518	0.273	0.743	2.137
beta4_pH[10,17]	0.733	0.278	0.348	0.688	1.287
beta4_pH[11,17]	0.691	0.245	0.351	0.647	1.186
beta4_pH[12,17]	0.912	0.366	0.433	0.825	1.708
beta4_pH[13,17]	0.738	0.266	0.378	0.693	1.290
beta4_pH[14,17]	1.039	0.336	0.565	0.985	1.690
beta4_pH[15,17]	0.890	0.257	0.533	0.849	1.429
beta4_pH[16,17]	0.875	0.358	0.419	0.789	1.642
beta4_pH[1,18]	0.718	0.285	0.309	0.670	1.295
beta4_pH[2,18]	0.878	0.215	0.550	0.866	1.267
beta4_pH[3,18]	0.888	0.197	0.548	0.858	1.372
beta4_pH[4,18]	0.824	0.262	0.435	0.789	1.348
beta4_pH[5,18]	0.567	0.484	0.083	0.408	1.854
beta4_pH[6,18]	1.603	1.355	0.231	1.272	5.773
beta4_pH[7,18]	1.115	0.606	0.352	0.970	2.479
beta4_pH[8,18]	0.770	0.435	0.227	0.678	1.731
beta4_pH[9,18]	0.866	0.512	0.275	0.733	2.146
beta4_pH[10,18]	0.743	0.275	0.351	0.708	1.282
beta4_pH[11,18]	0.689	0.247	0.352	0.646	1.186
beta4_pH[12,18]	0.939	0.384	0.438	0.851	1.730
beta4_pH[13,18]	0.745	0.263	0.379	0.700	1.279
beta4_pH[14,18]	1.030	0.337	0.561	0.977	1.705
beta4_pH[15,18]	0.927	0.266	0.539	0.893	1.448
beta4_pH[16,18]	0.887	0.357	0.418	0.810	1.661
beta4_pH[1,19]	0.725	0.288	0.308	0.689	1.292
beta4_pH[2,19]	0.913	0.215	0.554	0.915	1.269
beta4_pH[3,19]	0.897	0.202	0.547	0.872	1.412
beta4_pH[4,19]	0.835	0.271	0.435	0.799	1.351
beta4_pH[5,19]	0.580	0.494	0.083	0.412	1.860
beta4_pH[6,19]	1.718	1.469	0.237	1.316	6.158
beta4_pH[7,19]	1.197	0.628	0.353	1.083	2.545
beta4_pH[8,19]	0.755	0.425	0.226	0.653	1.706
beta4_pH[9,19]	0.932	0.544	0.276	0.796	2.188
beta4_pH[10,19]	0.754	0.279	0.349	0.719	1.308
beta4_pH[11,19]	0.676	0.239	0.352	0.633	1.177
beta4_pH[12,19]	0.943	0.380	0.443	0.862	1.732
beta4_pH[13,19]	0.756	0.264	0.379	0.712	1.286
beta4_pH[14,19]	1.021	0.334	0.564	0.961	1.696
beta4_pH[15,19]	0.936	0.268	0.541	0.906	1.451
beta4_pH[16,19]	0.890	0.359	0.417	0.815	1.647
beta4_pH[1,20]	0.710	0.286	0.304	0.667	1.287
beta4_pH[2,20]	0.911	0.214	0.553	0.905	1.272
beta4_pH[3,20]	0.934	0.200	0.602	0.906	1.404
beta4_pH[4,20]	0.824	0.272	0.433	0.785	1.346
beta4_pH[5,20]	0.662	0.532	0.085	0.508	1.987
beta4_pH[6,20]	1.708	1.436	0.236	1.327	6.023
beta4_pH[7,20]	1.134	0.628	0.348	0.977	2.526
beta4_pH[8,20]	0.743	0.422	0.225	0.648	1.719
beta4_pH[9,20]	0.984	0.572	0.276	0.833	2.227
beta4_pH[10,20]	0.733	0.278	0.345	0.689	1.294
beta4_pH[11,20]	0.679	0.247	0.349	0.636	1.185
beta4_pH[12,20]	0.941	0.379	0.439	0.856	1.715
beta4_pH[13,20]	0.754	0.266	0.383	0.708	1.298
beta4_pH[14,20]	1.032	0.336	0.558	0.976	1.696
beta4_pH[15,20]	0.919	0.266	0.538	0.879	1.436
beta4_pH[16,20]	0.896	0.366	0.419	0.819	1.654
beta4_pH[1,21]	0.687	0.278	0.305	0.640	1.280
beta4_pH[2,21]	0.866	0.210	0.546	0.846	1.261
beta4_pH[3,21]	0.913	0.198	0.571	0.885	1.416
beta4_pH[4,21]	0.805	0.267	0.431	0.771	1.345
beta4_pH[5,21]	0.650	0.531	0.085	0.485	1.947
beta4_pH[6,21]	1.675	1.453	0.230	1.274	5.943
beta4_pH[7,21]	1.014	0.585	0.339	0.853	2.434
beta4_pH[8,21]	0.777	0.441	0.227	0.684	1.747
beta4_pH[9,21]	0.945	0.551	0.273	0.809	2.216
beta4_pH[10,21]	0.725	0.279	0.345	0.680	1.295
beta4_pH[11,21]	0.681	0.244	0.351	0.637	1.186
beta4_pH[12,21]	0.941	0.380	0.437	0.860	1.740
beta4_pH[13,21]	0.742	0.264	0.377	0.691	1.286
beta4_pH[14,21]	1.016	0.339	0.556	0.959	1.700
beta4_pH[15,21]	0.899	0.265	0.535	0.845	1.440
beta4_pH[16,21]	0.898	0.362	0.416	0.828	1.667
beta4_pH[1,22]	0.691	0.285	0.303	0.643	1.283
beta4_pH[2,22]	0.855	0.203	0.549	0.832	1.253
beta4_pH[3,22]	0.829	0.160	0.539	0.817	1.199
beta4_pH[4,22]	0.862	0.271	0.441	0.838	1.359
beta4_pH[5,22]	0.523	0.442	0.083	0.381	1.712
beta4_pH[6,22]	1.501	1.281	0.229	1.199	5.331
beta4_pH[7,22]	0.975	0.570	0.343	0.813	2.412
beta4_pH[8,22]	0.770	0.429	0.228	0.678	1.716
beta4_pH[9,22]	0.914	0.536	0.277	0.771	2.181
beta4_pH[10,22]	0.720	0.280	0.343	0.665	1.297
beta4_pH[11,22]	0.683	0.247	0.351	0.640	1.191
beta4_pH[12,22]	0.923	0.373	0.438	0.828	1.719
beta4_pH[13,22]	0.764	0.269	0.380	0.720	1.292
beta4_pH[14,22]	1.029	0.333	0.565	0.977	1.691
beta4_pH[15,22]	0.912	0.262	0.536	0.875	1.434
beta4_pH[16,22]	0.897	0.360	0.420	0.823	1.658
beta4_pH[1,23]	0.654	0.273	0.307	0.592	1.262
beta4_pH[2,23]	0.939	0.208	0.562	0.947	1.275
beta4_pH[3,23]	0.947	0.194	0.607	0.916	1.421
beta4_pH[4,23]	0.834	0.272	0.434	0.806	1.341
beta4_pH[5,23]	0.690	0.552	0.084	0.534	2.007
beta4_pH[6,23]	1.718	1.462	0.235	1.309	5.910
beta4_pH[7,23]	1.084	0.604	0.345	0.943	2.485
beta4_pH[8,23]	0.733	0.412	0.225	0.655	1.702
beta4_pH[9,23]	0.915	0.531	0.273	0.777	2.176
beta4_pH[10,23]	0.741	0.285	0.344	0.701	1.291
beta4_pH[11,23]	0.689	0.246	0.352	0.646	1.193
beta4_pH[12,23]	0.895	0.363	0.439	0.807	1.707
beta4_pH[13,23]	0.747	0.268	0.380	0.699	1.287
beta4_pH[14,23]	1.030	0.330	0.558	0.985	1.698
beta4_pH[15,23]	0.900	0.262	0.538	0.860	1.439
beta4_pH[16,23]	0.876	0.357	0.419	0.792	1.649
beta4_pH[1,24]	0.679	0.281	0.306	0.626	1.271
beta4_pH[2,24]	0.913	0.218	0.554	0.909	1.272
beta4_pH[3,24]	0.898	0.175	0.591	0.879	1.326
beta4_pH[4,24]	0.884	0.269	0.444	0.874	1.362
beta4_pH[5,24]	0.604	0.498	0.086	0.454	1.888
beta4_pH[6,24]	1.646	1.414	0.238	1.289	5.963
beta4_pH[7,24]	1.071	0.601	0.346	0.916	2.478
beta4_pH[8,24]	0.712	0.401	0.224	0.618	1.666
beta4_pH[9,24]	0.923	0.537	0.276	0.774	2.184
beta4_pH[10,24]	0.728	0.277	0.344	0.687	1.290
beta4_pH[11,24]	0.676	0.243	0.350	0.626	1.192
beta4_pH[12,24]	0.955	0.387	0.440	0.878	1.737
beta4_pH[13,24]	0.747	0.269	0.379	0.696	1.298
beta4_pH[14,24]	1.032	0.330	0.564	0.986	1.685
beta4_pH[15,24]	0.941	0.269	0.542	0.907	1.449
beta4_pH[16,24]	0.901	0.355	0.419	0.836	1.647
beta4_pH[1,25]	0.793	0.297	0.315	0.775	1.310
beta4_pH[2,25]	0.900	0.218	0.548	0.891	1.270
beta4_pH[3,25]	1.000	0.205	0.674	0.963	1.459
beta4_pH[4,25]	0.823	0.267	0.432	0.788	1.339
beta4_pH[5,25]	0.606	0.501	0.084	0.439	1.888
beta4_pH[6,25]	1.587	1.315	0.240	1.270	5.465
beta4_pH[7,25]	1.083	0.604	0.350	0.935	2.465
beta4_pH[8,25]	0.750	0.420	0.224	0.658	1.711
beta4_pH[9,25]	0.954	0.554	0.278	0.809	2.202
beta4_pH[10,25]	0.750	0.278	0.350	0.714	1.298
beta4_pH[11,25]	0.660	0.239	0.350	0.605	1.182
beta4_pH[12,25]	0.931	0.382	0.439	0.851	1.735
beta4_pH[13,25]	0.764	0.265	0.383	0.730	1.300
beta4_pH[14,25]	1.034	0.333	0.562	0.984	1.698
beta4_pH[15,25]	0.926	0.264	0.540	0.897	1.443
beta4_pH[16,25]	0.910	0.362	0.419	0.843	1.659
beta4_pH[1,26]	0.733	0.289	0.313	0.699	1.295
beta4_pH[2,26]	0.939	0.212	0.557	0.950	1.280
beta4_pH[3,26]	0.906	0.185	0.590	0.880	1.357
beta4_pH[4,26]	0.773	0.263	0.429	0.718	1.338
beta4_pH[5,26]	0.601	0.502	0.086	0.442	1.872
beta4_pH[6,26]	1.804	1.529	0.234	1.376	6.245
beta4_pH[7,26]	1.126	0.622	0.350	0.991	2.498
beta4_pH[8,26]	0.774	0.434	0.227	0.677	1.742
beta4_pH[9,26]	0.906	0.535	0.278	0.763	2.168
beta4_pH[10,26]	0.724	0.275	0.345	0.680	1.288
beta4_pH[11,26]	0.712	0.249	0.351	0.676	1.193
beta4_pH[12,26]	0.914	0.375	0.434	0.823	1.716
beta4_pH[13,26]	0.777	0.269	0.383	0.741	1.299
beta4_pH[14,26]	1.041	0.337	0.564	0.983	1.699
beta4_pH[15,26]	0.950	0.269	0.543	0.923	1.449
beta4_pH[16,26]	0.936	0.372	0.423	0.871	1.666
beta4_pH[1,27]	0.735	0.289	0.308	0.703	1.288
beta4_pH[2,27]	0.958	0.210	0.561	0.978	1.275
beta4_pH[3,27]	0.981	0.198	0.649	0.949	1.442
beta4_pH[4,27]	0.792	0.271	0.428	0.740	1.334
beta4_pH[5,27]	0.664	0.535	0.084	0.516	1.961
beta4_pH[6,27]	1.736	1.493	0.239	1.313	6.079
beta4_pH[7,27]	1.098	0.613	0.348	0.946	2.470
beta4_pH[8,27]	0.779	0.448	0.226	0.675	1.751
beta4_pH[9,27]	0.910	0.528	0.273	0.772	2.162
beta4_pH[10,27]	0.772	0.285	0.351	0.748	1.306
beta4_pH[11,27]	0.713	0.247	0.356	0.676	1.192
beta4_pH[12,27]	0.947	0.383	0.437	0.857	1.728
beta4_pH[13,27]	0.798	0.271	0.390	0.760	1.307
beta4_pH[14,27]	1.033	0.334	0.569	0.985	1.704
beta4_pH[15,27]	0.974	0.269	0.544	0.948	1.453
beta4_pH[16,27]	0.946	0.372	0.425	0.882	1.671
beta4_pH[1,28]	0.729	0.288	0.309	0.696	1.290
beta4_pH[2,28]	0.901	0.213	0.550	0.894	1.267
beta4_pH[3,28]	0.747	0.139	0.511	0.745	1.028
beta4_pH[4,28]	0.781	0.265	0.431	0.724	1.326
beta4_pH[5,28]	0.459	0.403	0.081	0.314	1.621
beta4_pH[6,28]	1.742	1.472	0.234	1.320	6.110
beta4_pH[7,28]	1.045	0.581	0.348	0.891	2.453
beta4_pH[8,28]	0.799	0.439	0.229	0.708	1.744
beta4_pH[9,28]	0.931	0.536	0.277	0.795	2.163
beta4_pH[10,28]	0.771	0.282	0.353	0.746	1.297
beta4_pH[11,28]	0.692	0.244	0.354	0.650	1.199
beta4_pH[12,28]	0.950	0.384	0.439	0.868	1.747
beta4_pH[13,28]	0.721	0.261	0.379	0.663	1.285
beta4_pH[14,28]	1.039	0.336	0.566	0.982	1.701
beta4_pH[15,28]	0.824	0.241	0.531	0.758	1.405
beta4_pH[16,28]	0.877	0.353	0.418	0.793	1.633
beta4_pH[1,29]	0.712	0.290	0.309	0.670	1.290
beta4_pH[2,29]	0.923	0.215	0.552	0.933	1.274
beta4_pH[3,29]	0.915	0.186	0.586	0.891	1.365
beta4_pH[4,29]	0.760	0.258	0.427	0.705	1.331
beta4_pH[5,29]	0.461	0.387	0.081	0.335	1.557
beta4_pH[6,29]	1.813	1.581	0.232	1.346	6.518
beta4_pH[7,29]	1.071	0.612	0.344	0.909	2.508
beta4_pH[8,29]	0.746	0.424	0.228	0.641	1.737
beta4_pH[9,29]	0.902	0.530	0.275	0.759	2.157
beta4_pH[10,29]	0.735	0.279	0.347	0.701	1.287
beta4_pH[11,29]	0.692	0.246	0.353	0.647	1.186
beta4_pH[12,29]	0.944	0.381	0.439	0.867	1.728
beta4_pH[13,29]	0.781	0.271	0.383	0.739	1.297
beta4_pH[14,29]	1.041	0.337	0.565	0.986	1.700
beta4_pH[15,29]	0.946	0.269	0.540	0.921	1.441
beta4_pH[16,29]	0.903	0.356	0.422	0.834	1.635
beta4_pH[1,30]	0.763	0.292	0.311	0.735	1.306
beta4_pH[2,30]	0.883	0.212	0.551	0.866	1.266
beta4_pH[3,30]	0.869	0.164	0.566	0.857	1.246
beta4_pH[4,30]	0.759	0.259	0.428	0.705	1.316
beta4_pH[5,30]	0.425	0.368	0.081	0.299	1.486
beta4_pH[6,30]	1.749	1.526	0.239	1.309	6.325
beta4_pH[7,30]	1.133	0.622	0.349	0.981	2.492
beta4_pH[8,30]	0.758	0.423	0.224	0.671	1.717
beta4_pH[9,30]	0.938	0.551	0.276	0.791	2.196
beta4_pH[10,30]	0.752	0.280	0.348	0.713	1.291
beta4_pH[11,30]	0.644	0.231	0.348	0.594	1.170
beta4_pH[12,30]	0.942	0.379	0.440	0.867	1.733
beta4_pH[13,30]	0.788	0.268	0.388	0.754	1.302
beta4_pH[14,30]	1.025	0.337	0.560	0.967	1.695
beta4_pH[15,30]	0.886	0.250	0.535	0.844	1.414
beta4_pH[16,30]	0.778	0.310	0.414	0.691	1.561
beta4_pH[1,31]	0.727	0.286	0.312	0.689	1.298
beta4_pH[2,31]	0.846	0.207	0.543	0.820	1.257
beta4_pH[3,31]	0.846	0.168	0.543	0.837	1.241
beta4_pH[4,31]	0.752	0.259	0.427	0.693	1.326
beta4_pH[5,31]	0.432	0.368	0.080	0.306	1.480
beta4_pH[6,31]	1.711	1.483	0.235	1.297	6.105
beta4_pH[7,31]	1.005	0.583	0.342	0.839	2.423
beta4_pH[8,31]	0.762	0.423	0.226	0.666	1.720
beta4_pH[9,31]	0.944	0.550	0.275	0.804	2.219
beta4_pH[10,31]	0.723	0.277	0.347	0.675	1.287
beta4_pH[11,31]	0.625	0.221	0.348	0.579	1.149
beta4_pH[12,31]	0.874	0.365	0.434	0.772	1.723
beta4_pH[13,31]	0.628	0.216	0.375	0.576	1.197
beta4_pH[14,31]	1.071	0.335	0.566	1.035	1.712
beta4_pH[15,31]	0.860	0.247	0.535	0.810	1.408
beta4_pH[16,31]	0.741	0.287	0.413	0.670	1.511
beta4_pH[1,32]	0.740	0.287	0.309	0.707	1.292
beta4_pH[2,32]	0.790	0.186	0.542	0.754	1.213
beta4_pH[3,32]	0.838	0.163	0.537	0.830	1.224
beta4_pH[4,32]	0.798	0.263	0.431	0.749	1.342
beta4_pH[5,32]	0.653	0.526	0.085	0.493	1.946
beta4_pH[6,32]	1.774	1.503	0.240	1.343	6.265
beta4_pH[7,32]	1.029	0.593	0.343	0.869	2.448
beta4_pH[8,32]	0.770	0.427	0.225	0.674	1.728
beta4_pH[9,32]	0.955	0.549	0.278	0.822	2.216
beta4_pH[10,32]	0.681	0.257	0.343	0.633	1.259
beta4_pH[11,32]	0.592	0.202	0.347	0.542	1.092
beta4_pH[12,32]	0.860	0.344	0.436	0.771	1.687
beta4_pH[13,32]	0.730	0.248	0.383	0.683	1.270
beta4_pH[14,32]	1.020	0.331	0.561	0.970	1.703
beta4_pH[15,32]	0.830	0.230	0.534	0.778	1.379
beta4_pH[16,32]	0.842	0.340	0.416	0.756	1.623
beta4_pH[1,33]	0.733	0.282	0.312	0.704	1.289
beta4_pH[2,33]	0.711	0.146	0.538	0.678	1.075
beta4_pH[3,33]	0.815	0.140	0.545	0.813	1.109
beta4_pH[4,33]	0.804	0.266	0.432	0.763	1.343
beta4_pH[5,33]	0.495	0.417	0.081	0.370	1.637
beta4_pH[6,33]	1.529	1.278	0.236	1.236	5.384
beta4_pH[7,33]	1.122	0.627	0.346	0.969	2.496
beta4_pH[8,33]	0.758	0.428	0.224	0.666	1.732
beta4_pH[9,33]	0.856	0.511	0.272	0.720	2.146
beta4_pH[10,33]	0.649	0.248	0.344	0.595	1.241
beta4_pH[11,33]	0.586	0.195	0.349	0.543	1.085
beta4_pH[12,33]	0.831	0.355	0.434	0.722	1.692
beta4_pH[13,33]	0.638	0.217	0.375	0.592	1.173
beta4_pH[14,33]	1.070	0.334	0.569	1.027	1.709
beta4_pH[15,33]	0.808	0.221	0.533	0.758	1.348
beta4_pH[16,33]	0.687	0.253	0.411	0.621	1.365
beta4_pH[1,34]	0.601	0.241	0.302	0.547	1.189
beta4_pH[2,34]	0.765	0.170	0.540	0.736	1.164
beta4_pH[3,34]	0.816	0.138	0.544	0.817	1.105
beta4_pH[4,34]	0.801	0.266	0.431	0.753	1.340
beta4_pH[5,34]	0.513	0.438	0.082	0.372	1.723
beta4_pH[6,34]	1.364	1.150	0.229	1.106	4.621
beta4_pH[7,34]	1.107	0.606	0.349	0.966	2.496
beta4_pH[8,34]	0.740	0.421	0.224	0.637	1.730
beta4_pH[9,34]	0.904	0.533	0.272	0.774	2.162
beta4_pH[10,34]	0.564	0.201	0.339	0.511	1.096
beta4_pH[11,34]	0.572	0.193	0.346	0.526	1.068
beta4_pH[12,34]	0.609	0.228	0.425	0.533	1.343
beta4_pH[13,34]	0.687	0.230	0.380	0.643	1.222
beta4_pH[14,34]	1.006	0.325	0.562	0.950	1.684
beta4_pH[15,34]	0.835	0.233	0.532	0.793	1.378
beta4_pH[16,34]	0.709	0.272	0.413	0.632	1.443
beta4_pH[1,35]	0.405	0.137	0.195	0.384	0.744
beta4_pH[2,35]	0.769	0.076	0.630	0.764	0.932
beta4_pH[3,35]	1.024	0.131	0.786	1.017	1.298
beta4_pH[4,35]	0.555	0.197	0.268	0.524	1.013
beta4_pH[5,35]	0.130	0.101	0.027	0.103	0.407
beta4_pH[6,35]	0.816	0.664	0.143	0.626	2.618
beta4_pH[7,35]	2.357	1.923	0.444	1.839	7.660
beta4_pH[8,35]	0.532	0.262	0.193	0.473	1.197
beta4_pH[9,35]	0.630	0.542	0.104	0.470	2.004
beta4_pH[10,35]	0.602	0.118	0.399	0.591	0.859
beta4_pH[11,35]	0.764	0.191	0.460	0.739	1.191
beta4_pH[12,35]	1.265	0.865	0.355	1.034	3.422
beta4_pH[13,35]	0.719	0.103	0.541	0.709	0.941
beta4_pH[14,35]	0.811	0.259	0.426	0.768	1.415
beta4_pH[15,35]	0.888	0.115	0.679	0.879	1.129
beta4_pH[16,35]	0.509	0.192	0.227	0.482	0.979
beta4_pH[1,36]	0.898	0.180	0.594	0.884	1.303
beta4_pH[2,36]	0.848	0.102	0.666	0.843	1.064
beta4_pH[3,36]	0.888	0.128	0.658	0.878	1.159
beta4_pH[4,36]	0.754	0.222	0.414	0.723	1.263
beta4_pH[5,36]	0.415	0.366	0.063	0.315	1.383
beta4_pH[6,36]	5.172	4.053	0.904	3.738	16.371
beta4_pH[7,36]	1.093	0.612	0.364	0.950	2.638
beta4_pH[8,36]	0.956	0.410	0.394	0.871	1.954
beta4_pH[9,36]	0.538	0.399	0.129	0.439	1.579
beta4_pH[10,36]	0.446	0.116	0.264	0.431	0.718
beta4_pH[11,36]	0.546	0.100	0.376	0.536	0.767
beta4_pH[12,36]	0.654	0.326	0.249	0.589	1.478
beta4_pH[13,36]	0.773	0.117	0.565	0.765	1.022
beta4_pH[14,36]	1.051	0.374	0.541	0.983	1.956
beta4_pH[15,36]	0.957	0.132	0.723	0.947	1.245
beta4_pH[16,36]	0.881	0.288	0.458	0.835	1.578
beta4_pH[1,37]	0.748	0.155	0.491	0.736	1.082
beta4_pH[2,37]	0.762	0.079	0.621	0.759	0.924
beta4_pH[3,37]	0.945	0.118	0.740	0.940	1.192
beta4_pH[4,37]	0.710	0.207	0.393	0.678	1.196
beta4_pH[5,37]	0.708	0.651	0.107	0.559	2.253
beta4_pH[6,37]	2.373	2.196	0.321	1.757	8.456
beta4_pH[7,37]	1.250	0.868	0.309	1.036	3.283
beta4_pH[8,37]	0.979	0.408	0.415	0.903	2.002
beta4_pH[9,37]	1.803	1.886	0.210	1.197	7.089
beta4_pH[10,37]	0.748	0.133	0.523	0.738	1.042
beta4_pH[11,37]	0.821	0.162	0.552	0.804	1.191
beta4_pH[12,37]	0.758	0.481	0.217	0.639	2.035
beta4_pH[13,37]	0.594	0.085	0.442	0.588	0.781
beta4_pH[14,37]	0.929	0.333	0.467	0.875	1.719
beta4_pH[15,37]	0.703	0.099	0.530	0.698	0.921
beta4_pH[16,37]	0.595	0.158	0.338	0.578	0.939
beta4_pH[1,38]	0.695	0.130	0.470	0.680	0.969
beta4_pH[2,38]	0.704	0.076	0.563	0.700	0.861
beta4_pH[3,38]	0.874	0.125	0.650	0.867	1.133
beta4_pH[4,38]	0.882	0.232	0.514	0.846	1.402
beta4_pH[5,38]	0.435	0.282	0.099	0.363	1.163
beta4_pH[6,38]	2.136	2.320	0.179	1.407	8.538
beta4_pH[7,38]	0.502	0.299	0.149	0.432	1.286
beta4_pH[8,38]	0.771	0.302	0.345	0.719	1.514
beta4_pH[9,38]	1.460	1.018	0.361	1.190	4.239
beta4_pH[10,38]	0.715	0.146	0.470	0.703	1.044
beta4_pH[11,38]	0.491	0.110	0.307	0.483	0.742
beta4_pH[12,38]	0.556	0.342	0.183	0.479	1.386
beta4_pH[13,38]	0.867	0.162	0.596	0.850	1.231
beta4_pH[14,38]	0.994	0.392	0.468	0.914	1.999
beta4_pH[15,38]	0.847	0.093	0.680	0.842	1.042
beta4_pH[16,38]	0.940	0.354	0.428	0.875	1.795
beta4_pH[1,39]	0.677	0.128	0.458	0.669	0.960
beta4_pH[2,39]	0.854	0.094	0.687	0.849	1.053
beta4_pH[3,39]	0.857	0.107	0.666	0.850	1.080
beta4_pH[4,39]	0.840	0.271	0.438	0.800	1.501
beta4_pH[5,39]	1.129	1.081	0.133	0.812	3.884
beta4_pH[6,39]	0.294	0.273	0.033	0.210	1.023
beta4_pH[7,39]	1.878	1.651	0.313	1.406	6.290
beta4_pH[8,39]	1.405	0.801	0.457	1.216	3.588
beta4_pH[9,39]	1.996	1.639	0.356	1.538	6.449
beta4_pH[10,39]	0.728	0.182	0.436	0.704	1.160
beta4_pH[11,39]	0.663	0.153	0.420	0.646	1.012
beta4_pH[12,39]	0.618	0.339	0.217	0.541	1.486
beta4_pH[13,39]	0.699	0.108	0.510	0.692	0.932
beta4_pH[14,39]	0.850	0.281	0.433	0.812	1.525
beta4_pH[15,39]	1.001	0.105	0.813	0.996	1.224
beta4_pH[16,39]	0.871	0.327	0.396	0.827	1.679
beta4_pH[1,40]	0.706	0.107	0.518	0.697	0.937
beta4_pH[2,40]	0.751	0.079	0.606	0.745	0.914
beta4_pH[3,40]	0.949	0.125	0.726	0.941	1.215
beta4_pH[4,40]	0.887	0.208	0.559	0.864	1.346
beta4_pH[5,40]	0.283	0.178	0.074	0.238	0.730
beta4_pH[6,40]	0.956	0.905	0.174	0.726	3.075
beta4_pH[7,40]	1.528	1.269	0.251	1.167	4.969
beta4_pH[8,40]	0.359	0.268	0.076	0.288	1.044
beta4_pH[9,40]	0.504	0.521	0.075	0.356	1.847
beta4_pH[10,40]	0.881	0.212	0.546	0.856	1.371
beta4_pH[11,40]	0.442	0.101	0.274	0.431	0.666
beta4_pH[12,40]	0.649	0.374	0.208	0.556	1.613
beta4_pH[13,40]	0.776	0.116	0.574	0.766	1.026
beta4_pH[14,40]	0.672	0.212	0.351	0.642	1.166
beta4_pH[15,40]	0.845	0.096	0.673	0.841	1.045
beta4_pH[16,40]	1.320	0.491	0.592	1.239	2.474
beta4_pH[1,41]	0.576	0.108	0.396	0.567	0.815
beta4_pH[2,41]	0.780	0.096	0.610	0.776	0.975
beta4_pH[3,41]	0.890	0.121	0.674	0.884	1.143
beta4_pH[4,41]	0.848	0.352	0.368	0.781	1.757
beta4_pH[5,41]	1.164	0.505	0.426	1.075	2.334
beta4_pH[6,41]	3.594	3.165	0.391	2.622	12.451
beta4_pH[7,41]	0.831	0.489	0.258	0.716	2.056
beta4_pH[8,41]	1.252	0.723	0.367	1.087	3.114
beta4_pH[9,41]	0.492	0.560	0.057	0.332	1.837
beta4_pH[10,41]	0.753	0.152	0.496	0.739	1.091
beta4_pH[11,41]	0.864	0.232	0.485	0.838	1.407
beta4_pH[12,41]	0.948	0.458	0.373	0.847	2.090
beta4_pH[13,41]	0.672	0.103	0.490	0.665	0.901
beta4_pH[14,41]	1.077	0.325	0.579	1.036	1.834
beta4_pH[15,41]	0.784	0.097	0.615	0.778	0.995
beta4_pH[16,41]	1.113	0.479	0.449	1.025	2.351
beta4_pH[1,42]	0.608	0.111	0.419	0.600	0.854
beta4_pH[2,42]	0.781	0.093	0.618	0.775	0.981
beta4_pH[3,42]	0.802	0.131	0.571	0.793	1.079
beta4_pH[4,42]	0.983	0.320	0.507	0.929	1.749
beta4_pH[5,42]	1.605	1.683	0.183	1.094	6.430
beta4_pH[6,42]	0.222	0.137	0.054	0.188	0.591
beta4_pH[7,42]	0.980	0.627	0.272	0.833	2.474
beta4_pH[8,42]	0.777	0.324	0.323	0.713	1.554
beta4_pH[9,42]	0.787	0.553	0.175	0.632	2.251
beta4_pH[10,42]	0.850	0.169	0.563	0.836	1.218
beta4_pH[11,42]	0.663	0.141	0.426	0.649	0.983
beta4_pH[12,42]	0.852	0.384	0.340	0.772	1.787
beta4_pH[13,42]	0.503	0.151	0.270	0.481	0.867
beta4_pH[14,42]	0.892	0.300	0.443	0.848	1.606
beta4_pH[15,42]	0.928	0.093	0.762	0.925	1.119
beta4_pH[16,42]	0.629	0.210	0.309	0.602	1.126
beta4_pH[1,43]	0.716	0.148	0.461	0.704	1.041
beta4_pH[2,43]	0.741	0.075	0.606	0.737	0.898
beta4_pH[3,43]	0.634	0.080	0.492	0.630	0.802
beta4_pH[4,43]	0.859	0.283	0.439	0.813	1.503
beta4_pH[5,43]	1.565	0.662	0.626	1.441	3.153
beta4_pH[6,43]	1.054	0.595	0.254	0.942	2.481
beta4_pH[7,43]	0.732	0.619	0.142	0.567	2.296
beta4_pH[8,43]	0.576	0.245	0.240	0.532	1.199
beta4_pH[9,43]	1.190	1.081	0.193	0.853	4.237
beta4_pH[10,43]	0.632	0.125	0.424	0.618	0.906
beta4_pH[11,43]	0.662	0.136	0.435	0.649	0.969
beta4_pH[12,43]	0.790	0.394	0.297	0.706	1.752
beta4_pH[13,43]	0.604	0.122	0.400	0.591	0.867
beta4_pH[14,43]	1.091	0.345	0.586	1.036	1.901
beta4_pH[15,43]	0.846	0.101	0.663	0.842	1.058
beta4_pH[16,43]	1.266	0.434	0.639	1.194	2.359
beta4_pH[1,44]	0.555	0.117	0.353	0.547	0.811
beta4_pH[2,44]	0.696	0.073	0.561	0.693	0.852
beta4_pH[3,44]	0.622	0.088	0.467	0.619	0.802
beta4_pH[4,44]	0.839	0.201	0.515	0.815	1.303
beta4_pH[5,44]	0.951	0.375	0.399	0.890	1.836
beta4_pH[6,44]	0.865	0.810	0.121	0.693	2.570
beta4_pH[7,44]	1.199	0.700	0.364	1.033	2.899
beta4_pH[8,44]	0.374	0.202	0.112	0.334	0.868
beta4_pH[9,44]	1.016	0.932	0.169	0.742	3.596
beta4_pH[10,44]	0.573	0.119	0.367	0.564	0.833
beta4_pH[11,44]	0.348	0.117	0.170	0.330	0.629
beta4_pH[12,44]	0.639	0.313	0.218	0.573	1.415
beta4_pH[13,44]	0.541	0.095	0.379	0.535	0.752
beta4_pH[14,44]	0.679	0.181	0.390	0.656	1.096
beta4_pH[15,44]	0.638	0.087	0.485	0.631	0.826
beta4_pH[16,44]	0.452	0.175	0.196	0.424	0.857
beta4_pH[1,45]	0.731	0.152	0.479	0.716	1.075
beta4_pH[2,45]	0.692	0.080	0.545	0.688	0.863
beta4_pH[3,45]	0.734	0.114	0.535	0.725	0.980
beta4_pH[4,45]	0.753	0.181	0.462	0.731	1.169
beta4_pH[5,45]	0.954	0.959	0.105	0.674	3.532
beta4_pH[6,45]	0.914	0.664	0.210	0.780	2.434
beta4_pH[7,45]	0.712	0.574	0.129	0.558	2.198
beta4_pH[8,45]	1.142	0.510	0.471	1.042	2.409
beta4_pH[9,45]	0.104	0.115	0.010	0.067	0.407
beta4_pH[10,45]	0.787	0.172	0.499	0.769	1.175
beta4_pH[11,45]	0.483	0.106	0.310	0.474	0.721
beta4_pH[12,45]	0.793	0.339	0.313	0.734	1.618
beta4_pH[13,45]	0.465	0.076	0.336	0.458	0.629
beta4_pH[14,45]	0.729	0.180	0.446	0.702	1.146
beta4_pH[15,45]	0.508	0.071	0.384	0.502	0.658
beta4_pH[16,45]	0.331	0.182	0.098	0.292	0.787
beta4_pH[1,46]	0.726	0.126	0.513	0.714	1.008
beta4_pH[2,46]	0.655	0.084	0.508	0.648	0.835
beta4_pH[3,46]	0.793	0.111	0.602	0.787	1.028
beta4_pH[4,46]	0.855	0.295	0.429	0.805	1.582
beta4_pH[5,46]	0.870	0.377	0.330	0.806	1.776
beta4_pH[6,46]	1.737	1.973	0.157	1.136	7.396
beta4_pH[7,46]	1.722	1.242	0.389	1.404	4.935
beta4_pH[8,46]	0.912	0.411	0.379	0.821	1.960
beta4_pH[9,46]	1.486	1.483	0.200	1.056	5.443
beta4_pH[10,46]	0.648	0.156	0.391	0.630	0.996
beta4_pH[11,46]	0.683	0.138	0.444	0.675	0.981
beta4_pH[12,46]	0.997	0.385	0.385	0.950	1.867
beta4_pH[13,46]	0.587	0.177	0.312	0.561	0.990
beta4_pH[14,46]	0.909	0.271	0.458	0.879	1.495
beta4_pH[15,46]	0.606	0.071	0.477	0.603	0.757
beta4_pH[16,46]	0.608	0.208	0.282	0.581	1.105
beta4_pH[1,47]	0.603	0.117	0.402	0.592	0.852
beta4_pH[2,47]	0.753	0.101	0.572	0.748	0.966
beta4_pH[3,47]	0.761	0.101	0.580	0.753	0.971
beta4_pH[4,47]	0.575	0.231	0.252	0.538	1.149
beta4_pH[5,47]	0.141	0.130	0.025	0.107	0.466
beta4_pH[6,47]	0.167	0.106	0.040	0.142	0.445
beta4_pH[7,47]	0.490	0.431	0.081	0.365	1.732
beta4_pH[8,47]	0.948	0.614	0.246	0.805	2.547
beta4_pH[9,47]	0.443	0.532	0.038	0.281	1.810
beta4_pH[10,47]	0.767	0.207	0.438	0.744	1.227
beta4_pH[11,47]	0.585	0.115	0.390	0.576	0.835
beta4_pH[12,47]	1.135	0.400	0.452	1.116	1.980
beta4_pH[13,47]	0.684	0.113	0.489	0.675	0.927
beta4_pH[14,47]	0.830	0.293	0.395	0.785	1.497
beta4_pH[15,47]	0.692	0.110	0.501	0.682	0.928
beta4_pH[16,47]	0.704	0.205	0.360	0.683	1.152
beta0_pelagic[1]	2.248	0.140	1.978	2.248	2.534
beta0_pelagic[2]	1.484	0.125	1.243	1.481	1.731
beta0_pelagic[3]	0.210	0.252	-0.318	0.230	0.657
beta0_pelagic[4]	0.123	0.400	-0.819	0.175	0.752
beta0_pelagic[5]	1.436	0.209	1.019	1.433	1.834
beta0_pelagic[6]	1.370	0.155	1.067	1.369	1.685
beta0_pelagic[7]	1.508	0.147	1.224	1.507	1.797
beta0_pelagic[8]	1.739	0.147	1.445	1.734	2.033
beta0_pelagic[9]	2.640	0.169	2.327	2.635	2.968
beta0_pelagic[10]	2.533	0.139	2.252	2.534	2.808
beta0_pelagic[11]	-0.323	0.231	-0.867	-0.310	0.088
beta0_pelagic[12]	1.712	0.144	1.439	1.712	1.997
beta0_pelagic[13]	0.135	0.425	-1.150	0.260	0.648
beta0_pelagic[14]	-0.334	0.310	-1.077	-0.293	0.175
beta0_pelagic[15]	-0.314	0.223	-1.023	-0.285	0.002
beta0_pelagic[16]	-0.330	0.320	-1.082	-0.310	0.214
beta1_pelagic[1]	0.000	0.000	0.000	0.000	0.000
beta1_pelagic[2]	0.000	0.000	0.000	0.000	0.000
beta1_pelagic[3]	0.673	0.275	0.115	0.671	1.221
beta1_pelagic[4]	1.011	0.432	0.292	0.964	2.039
beta1_pelagic[5]	0.000	0.000	0.000	0.000	0.000
beta1_pelagic[6]	0.000	0.000	0.000	0.000	0.000
beta1_pelagic[7]	0.000	0.000	0.000	0.000	0.000
beta1_pelagic[8]	0.000	0.000	0.000	0.000	0.000
beta1_pelagic[9]	0.000	0.000	0.000	0.000	0.000
beta1_pelagic[10]	0.000	0.000	0.000	0.000	0.000
beta1_pelagic[11]	1.417	0.287	0.895	1.400	2.036
beta1_pelagic[12]	0.000	0.000	0.000	0.000	0.000
beta1_pelagic[13]	1.025	0.692	0.031	0.861	2.721
beta1_pelagic[14]	1.733	0.522	0.914	1.654	2.837
beta1_pelagic[15]	0.157	0.216	0.011	0.065	0.806
beta1_pelagic[16]	1.402	0.478	0.641	1.336	2.630
beta2_pelagic[1]	0.000	0.000	0.000	0.000	0.000
beta2_pelagic[2]	0.000	0.000	0.000	0.000	0.000
beta2_pelagic[3]	7.046	5.974	0.237	5.633	21.132
beta2_pelagic[4]	6.516	5.840	0.298	4.901	20.897
beta2_pelagic[5]	0.000	0.000	0.000	0.000	0.000
beta2_pelagic[6]	0.000	0.000	0.000	0.000	0.000
beta2_pelagic[7]	0.000	0.000	0.000	0.000	0.000
beta2_pelagic[8]	0.000	0.000	0.000	0.000	0.000
beta2_pelagic[9]	0.000	0.000	0.000	0.000	0.000
beta2_pelagic[10]	0.000	0.000	0.000	0.000	0.000
beta2_pelagic[11]	2.301	1.726	0.295	1.824	6.600
beta2_pelagic[12]	0.000	0.000	0.000	0.000	0.000
beta2_pelagic[13]	1.687	1.727	0.085	1.057	6.186
beta2_pelagic[14]	1.131	1.274	0.167	0.634	4.817
beta2_pelagic[15]	2.479	1.926	0.087	2.085	7.241
beta2_pelagic[16]	2.667	2.657	0.167	1.603	9.589
beta3_pelagic[1]	28.951	6.321	18.471	29.017	39.427
beta3_pelagic[2]	29.022	6.441	18.571	28.873	39.435
beta3_pelagic[3]	27.945	3.283	22.468	27.975	35.191
beta3_pelagic[4]	24.872	2.058	20.888	24.991	28.569
beta3_pelagic[5]	29.038	6.366	18.541	29.189	39.471
beta3_pelagic[6]	29.089	6.362	18.561	29.029	39.486
beta3_pelagic[7]	28.926	6.272	18.642	28.829	39.380
beta3_pelagic[8]	29.085	6.411	18.541	29.407	39.481
beta3_pelagic[9]	29.120	6.285	18.536	29.525	39.261
beta3_pelagic[10]	29.010	6.350	18.417	29.165	39.444
beta3_pelagic[11]	29.774	1.257	27.506	29.730	32.397
beta3_pelagic[12]	28.837	6.368	18.551	28.746	39.421
beta3_pelagic[13]	34.020	4.877	21.194	35.273	39.817
beta3_pelagic[14]	33.959	2.049	30.304	33.881	38.400
beta3_pelagic[15]	29.828	6.843	18.445	30.543	39.756
beta3_pelagic[16]	31.385	1.972	27.966	31.078	36.180
beta0_yellow[1]	-0.509	0.161	-0.823	-0.510	-0.194
beta0_yellow[2]	0.575	0.174	0.217	0.583	0.889
beta0_yellow[3]	-0.161	0.216	-0.591	-0.147	0.214
beta0_yellow[4]	0.923	0.366	-0.333	0.994	1.348
beta0_yellow[5]	0.416	0.333	-0.333	0.461	0.947
beta0_yellow[6]	0.809	0.164	0.492	0.806	1.138
beta0_yellow[7]	0.916	0.163	0.605	0.909	1.236
beta0_yellow[8]	0.970	0.167	0.657	0.964	1.313
beta0_yellow[9]	0.563	0.169	0.217	0.567	0.875
beta0_yellow[10]	0.691	0.141	0.415	0.695	0.957
beta0_yellow[11]	0.202	0.177	-0.140	0.199	0.552
beta0_yellow[12]	-1.121	0.178	-1.473	-1.116	-0.785
beta0_yellow[13]	-0.843	0.170	-1.177	-0.844	-0.513
beta0_yellow[14]	0.018	0.180	-0.337	0.017	0.371
beta0_yellow[15]	-0.805	0.170	-1.155	-0.798	-0.474
beta0_yellow[16]	-0.237	0.176	-0.575	-0.237	0.102
beta1_yellow[1]	0.000	0.000	0.000	0.000	0.000
beta1_yellow[2]	0.994	0.317	0.471	0.972	1.583
beta1_yellow[3]	0.442	0.334	0.014	0.432	1.033
beta1_yellow[4]	1.257	0.727	0.450	1.101	3.727
beta1_yellow[5]	0.000	0.000	0.000	0.000	0.000
beta1_yellow[6]	0.000	0.000	0.000	0.000	0.000
beta1_yellow[7]	0.000	0.000	0.000	0.000	0.000
beta1_yellow[8]	0.000	0.000	0.000	0.000	0.000
beta1_yellow[9]	0.000	0.000	0.000	0.000	0.000
beta1_yellow[10]	0.000	0.000	0.000	0.000	0.000
beta1_yellow[11]	0.000	0.000	0.000	0.000	0.000
beta1_yellow[12]	0.000	0.000	0.000	0.000	0.000
beta1_yellow[13]	0.000	0.000	0.000	0.000	0.000
beta1_yellow[14]	0.000	0.000	0.000	0.000	0.000
beta1_yellow[15]	0.000	0.000	0.000	0.000	0.000
beta1_yellow[16]	0.000	0.000	0.000	0.000	0.000
beta2_yellow[1]	0.000	0.000	0.000	0.000	0.000
beta2_yellow[2]	-7.416	5.661	-21.109	-6.225	-0.298
beta2_yellow[3]	-7.624	5.909	-21.883	-6.264	-0.287
beta2_yellow[4]	-6.007	5.420	-19.567	-4.646	-0.097
beta2_yellow[5]	0.000	0.000	0.000	0.000	0.000
beta2_yellow[6]	0.000	0.000	0.000	0.000	0.000
beta2_yellow[7]	0.000	0.000	0.000	0.000	0.000
beta2_yellow[8]	0.000	0.000	0.000	0.000	0.000
beta2_yellow[9]	0.000	0.000	0.000	0.000	0.000
beta2_yellow[10]	0.000	0.000	0.000	0.000	0.000
beta2_yellow[11]	0.000	0.000	0.000	0.000	0.000
beta2_yellow[12]	0.000	0.000	0.000	0.000	0.000
beta2_yellow[13]	0.000	0.000	0.000	0.000	0.000
beta2_yellow[14]	0.000	0.000	0.000	0.000	0.000
beta2_yellow[15]	0.000	0.000	0.000	0.000	0.000
beta2_yellow[16]	0.000	0.000	0.000	0.000	0.000
beta3_yellow[1]	25.000	0.000	25.000	25.000	25.000
beta3_yellow[2]	28.984	1.539	26.809	28.746	32.789
beta3_yellow[3]	32.237	4.182	20.663	32.719	39.931
beta3_yellow[4]	28.888	3.405	23.030	27.812	36.543
beta3_yellow[5]	25.000	0.000	25.000	25.000	25.000
beta3_yellow[6]	25.000	0.000	25.000	25.000	25.000
beta3_yellow[7]	25.000	0.000	25.000	25.000	25.000
beta3_yellow[8]	25.000	0.000	25.000	25.000	25.000
beta3_yellow[9]	25.000	0.000	25.000	25.000	25.000
beta3_yellow[10]	25.000	0.000	25.000	25.000	25.000
beta3_yellow[11]	25.000	0.000	25.000	25.000	25.000
beta3_yellow[12]	25.000	0.000	25.000	25.000	25.000
beta3_yellow[13]	25.000	0.000	25.000	25.000	25.000
beta3_yellow[14]	25.000	0.000	25.000	25.000	25.000
beta3_yellow[15]	25.000	0.000	25.000	25.000	25.000
beta3_yellow[16]	25.000	0.000	25.000	25.000	25.000
beta0_black[1]	-0.003	0.152	-0.298	-0.002	0.289
beta0_black[2]	1.890	0.137	1.630	1.890	2.157
beta0_black[3]	1.375	0.143	1.084	1.378	1.655
beta0_black[4]	2.488	0.141	2.215	2.490	2.762
beta0_black[5]	4.570	2.198	1.786	4.074	10.018
beta0_black[6]	4.418	1.942	2.095	3.909	9.314
beta0_black[7]	3.201	1.713	1.312	2.763	8.124
beta0_black[8]	0.904	0.232	0.454	0.895	1.360
beta0_black[9]	2.586	0.262	2.053	2.587	3.101
beta0_black[10]	1.370	0.138	1.092	1.371	1.648
beta0_black[11]	3.466	0.170	3.131	3.469	3.802
beta0_black[12]	4.853	0.200	4.469	4.850	5.252
beta0_black[13]	0.243	0.189	0.009	0.203	0.687
beta0_black[14]	2.983	0.178	2.625	2.977	3.339
beta0_black[15]	1.405	0.175	1.077	1.402	1.754
beta0_black[16]	4.249	0.177	3.900	4.251	4.598
beta2_black[1]	0.000	0.000	0.000	0.000	0.000
beta2_black[2]	0.000	0.000	0.000	0.000	0.000
beta2_black[3]	0.000	0.000	0.000	0.000	0.000
beta2_black[4]	0.000	0.000	0.000	0.000	0.000
beta2_black[5]	0.000	0.000	0.000	0.000	0.000
beta2_black[6]	0.000	0.000	0.000	0.000	0.000
beta2_black[7]	0.000	0.000	0.000	0.000	0.000
beta2_black[8]	0.000	0.000	0.000	0.000	0.000
beta2_black[9]	0.000	0.000	0.000	0.000	0.000
beta2_black[10]	0.000	0.000	0.000	0.000	0.000
beta2_black[11]	0.000	0.000	0.000	0.000	0.000
beta2_black[12]	0.000	0.000	0.000	0.000	0.000
beta2_black[13]	-2.392	1.571	-6.348	-1.977	-0.511
beta2_black[14]	0.000	0.000	0.000	0.000	0.000
beta2_black[15]	0.000	0.000	0.000	0.000	0.000
beta2_black[16]	0.000	0.000	0.000	0.000	0.000
beta3_black[1]	25.000	0.000	25.000	25.000	25.000
beta3_black[2]	25.000	0.000	25.000	25.000	25.000
beta3_black[3]	25.000	0.000	25.000	25.000	25.000
beta3_black[4]	25.000	0.000	25.000	25.000	25.000
beta3_black[5]	25.000	0.000	25.000	25.000	25.000
beta3_black[6]	25.000	0.000	25.000	25.000	25.000
beta3_black[7]	25.000	0.000	25.000	25.000	25.000
beta3_black[8]	25.000	0.000	25.000	25.000	25.000
beta3_black[9]	25.000	0.000	25.000	25.000	25.000
beta3_black[10]	25.000	0.000	25.000	25.000	25.000
beta3_black[11]	25.000	0.000	25.000	25.000	25.000
beta3_black[12]	25.000	0.000	25.000	25.000	25.000
beta3_black[13]	38.934	0.946	36.868	39.104	40.304
beta3_black[14]	25.000	0.000	25.000	25.000	25.000
beta3_black[15]	25.000	0.000	25.000	25.000	25.000
beta3_black[16]	25.000	0.000	25.000	25.000	25.000
beta4_black[1]	-0.262	0.204	-0.652	-0.265	0.140
beta4_black[2]	0.267	0.192	-0.094	0.266	0.640
beta4_black[3]	-1.007	0.194	-1.381	-1.006	-0.608
beta4_black[4]	0.490	0.217	0.087	0.490	0.926
beta4_black[5]	0.729	1.550	-1.164	0.414	4.518
beta4_black[6]	0.788	1.393	-0.949	0.484	4.337
beta4_black[7]	0.654	1.361	-1.060	0.380	3.984
beta4_black[8]	-0.238	0.322	-0.871	-0.236	0.373
beta4_black[9]	0.951	0.832	-0.208	0.783	3.102
beta4_black[10]	0.061	0.185	-0.300	0.061	0.429
beta4_black[11]	-0.712	0.228	-1.165	-0.708	-0.270
beta4_black[12]	0.412	0.332	-0.243	0.411	1.081
beta4_black[13]	-1.348	0.219	-1.779	-1.343	-0.914
beta4_black[14]	-0.114	0.249	-0.589	-0.119	0.385
beta4_black[15]	-0.929	0.226	-1.374	-0.926	-0.478
beta4_black[16]	-0.602	0.251	-1.103	-0.601	-0.104
beta0_dsr[11]	1.888	0.174	1.552	1.883	2.249
beta0_dsr[12]	4.985	0.276	4.486	4.976	5.546
beta0_dsr[13]	1.521	0.166	1.198	1.517	1.858
beta0_dsr[14]	2.619	0.186	2.265	2.616	2.988
beta0_dsr[15]	1.335	0.166	1.015	1.338	1.660
beta0_dsr[16]	2.833	0.180	2.487	2.832	3.190
beta1_dsr[11]	0.000	0.000	0.000	0.000	0.000
beta1_dsr[12]	0.000	0.000	0.000	0.000	0.000
beta1_dsr[13]	0.000	0.000	0.000	0.000	0.000
beta1_dsr[14]	0.000	0.000	0.000	0.000	0.000
beta1_dsr[15]	0.000	0.000	0.000	0.000	0.000
beta1_dsr[16]	0.000	0.000	0.000	0.000	0.000
beta4_dsr[11]	0.671	0.238	0.206	0.670	1.136
beta4_dsr[12]	0.007	0.730	-1.263	-0.049	1.634
beta4_dsr[13]	-0.331	0.228	-0.790	-0.329	0.112
beta4_dsr[14]	0.053	0.285	-0.505	0.051	0.606
beta4_dsr[15]	0.822	0.221	0.384	0.816	1.258
beta4_dsr[16]	0.086	0.256	-0.405	0.089	0.599
beta0_slope[11]	-1.828	0.172	-2.153	-1.825	-1.477
beta0_slope[12]	-4.748	0.258	-5.251	-4.748	-4.249
beta0_slope[13]	-1.264	0.171	-1.599	-1.260	-0.934
beta0_slope[14]	-2.628	0.184	-2.978	-2.628	-2.258
beta0_slope[15]	-1.257	0.170	-1.593	-1.253	-0.929
beta0_slope[16]	-2.678	0.178	-3.025	-2.680	-2.330
beta1_slope[11]	0.000	0.000	0.000	0.000	0.000
beta1_slope[12]	0.000	0.000	0.000	0.000	0.000
beta1_slope[13]	0.000	0.000	0.000	0.000	0.000
beta1_slope[14]	0.000	0.000	0.000	0.000	0.000
beta1_slope[15]	0.000	0.000	0.000	0.000	0.000
beta1_slope[16]	0.000	0.000	0.000	0.000	0.000
beta4_slope[11]	-0.810	0.232	-1.265	-0.807	-0.371
beta4_slope[12]	-1.619	0.602	-2.861	-1.589	-0.479
beta4_slope[13]	0.074	0.228	-0.367	0.073	0.511
beta4_slope[14]	0.014	0.275	-0.526	0.022	0.537
beta4_slope[15]	-0.890	0.228	-1.327	-0.891	-0.434
beta4_slope[16]	-0.230	0.243	-0.712	-0.228	0.246
beta5_slope[11]	2.677	0.284	2.131	2.672	3.221
beta5_slope[12]	-0.208	0.461	-1.153	-0.203	0.678
beta5_slope[13]	1.235	0.273	0.712	1.239	1.771
beta5_slope[14]	4.026	0.511	3.052	4.014	5.060
beta5_slope[15]	1.755	0.288	1.203	1.756	2.319
beta5_slope[16]	2.679	0.355	1.995	2.672	3.385
sigma_H[1]	0.223	0.056	0.128	0.218	0.348
sigma_H[2]	0.168	0.030	0.117	0.165	0.235
sigma_H[3]	0.196	0.042	0.120	0.194	0.286
sigma_H[4]	0.422	0.077	0.295	0.414	0.600
sigma_H[5]	1.053	0.211	0.684	1.041	1.509
sigma_H[6]	0.404	0.197	0.034	0.403	0.795
sigma_H[7]	0.304	0.062	0.211	0.297	0.449
sigma_H[8]	0.409	0.090	0.252	0.402	0.600
sigma_H[9]	0.524	0.125	0.327	0.508	0.796
sigma_H[10]	0.213	0.040	0.144	0.210	0.300
sigma_H[11]	0.275	0.046	0.197	0.271	0.374
sigma_H[12]	0.436	0.165	0.208	0.410	0.771
sigma_H[13]	0.219	0.037	0.156	0.215	0.302
sigma_H[14]	0.515	0.093	0.354	0.509	0.713
sigma_H[15]	0.245	0.040	0.180	0.241	0.332
sigma_H[16]	0.228	0.044	0.155	0.224	0.330
lambda_H[1]	2.796	3.717	0.133	1.567	12.349
lambda_H[2]	6.686	6.237	0.603	4.914	22.928
lambda_H[3]	6.823	10.895	0.304	3.239	36.878
lambda_H[4]	0.006	0.004	0.001	0.005	0.017
lambda_H[5]	3.835	8.700	0.036	0.953	28.491
lambda_H[6]	7.376	15.025	0.008	0.623	48.944
lambda_H[7]	0.013	0.009	0.002	0.011	0.036
lambda_H[8]	8.230	9.785	0.166	4.861	35.607
lambda_H[9]	0.015	0.010	0.003	0.013	0.040
lambda_H[10]	0.278	0.500	0.032	0.186	1.035
lambda_H[11]	0.256	0.366	0.012	0.133	1.199
lambda_H[12]	4.516	5.992	0.197	2.540	21.139
lambda_H[13]	3.337	3.065	0.244	2.458	11.773
lambda_H[14]	3.344	3.906	0.225	2.089	14.212
lambda_H[15]	0.026	0.050	0.004	0.017	0.102
lambda_H[16]	1.350	1.721	0.077	0.808	5.795
mu_lambda_H[1]	4.287	1.924	1.178	4.103	8.403
mu_lambda_H[2]	3.866	1.917	0.659	3.706	7.966
mu_lambda_H[3]	3.485	1.816	0.821	3.218	7.559
sigma_lambda_H[1]	8.529	4.361	2.033	7.921	18.388
sigma_lambda_H[2]	8.501	4.618	1.045	8.056	18.448
sigma_lambda_H[3]	6.112	3.929	1.036	5.197	16.072
beta_H[1,1]	6.881	1.131	4.182	7.071	8.585
beta_H[2,1]	9.851	0.543	8.672	9.877	10.894
beta_H[3,1]	7.968	0.754	6.220	8.058	9.186
beta_H[4,1]	9.156	7.954	-7.155	9.499	24.047
beta_H[5,1]	0.208	2.410	-4.771	0.400	4.311
beta_H[6,1]	3.052	4.011	-7.220	4.497	7.465
beta_H[7,1]	0.797	5.778	-11.573	1.085	11.449
beta_H[8,1]	1.180	2.526	-2.209	1.250	3.282
beta_H[9,1]	13.083	5.561	1.733	13.023	24.231
beta_H[10,1]	7.012	1.732	3.325	7.073	10.215
beta_H[11,1]	5.124	3.465	-2.728	5.842	9.910
beta_H[12,1]	2.636	1.053	0.771	2.578	5.020
beta_H[13,1]	9.021	0.928	7.054	9.097	10.468
beta_H[14,1]	2.159	1.043	0.123	2.161	4.188
beta_H[15,1]	-6.053	3.800	-12.917	-6.290	2.216
beta_H[16,1]	3.010	2.133	-0.729	2.859	7.728
beta_H[1,2]	7.875	0.257	7.340	7.880	8.352
beta_H[2,2]	10.002	0.146	9.708	10.003	10.284
beta_H[3,2]	8.930	0.194	8.549	8.933	9.310
beta_H[4,2]	3.603	1.504	0.842	3.536	6.799
beta_H[5,2]	2.067	0.967	0.075	2.104	3.873
beta_H[6,2]	5.769	1.039	3.300	5.937	7.380
beta_H[7,2]	2.618	1.100	0.668	2.542	4.947
beta_H[8,2]	3.075	0.839	1.637	3.163	4.211
beta_H[9,2]	3.479	1.110	1.388	3.443	5.747
beta_H[10,2]	8.190	0.347	7.482	8.202	8.852
beta_H[11,2]	9.783	0.616	8.866	9.659	11.176
beta_H[12,2]	3.951	0.369	3.260	3.932	4.717
beta_H[13,2]	9.103	0.256	8.639	9.087	9.612
beta_H[14,2]	4.009	0.354	3.337	3.997	4.704
beta_H[15,2]	11.345	0.679	9.862	11.366	12.588
beta_H[16,2]	4.635	0.763	3.122	4.650	6.096
beta_H[1,3]	8.422	0.259	7.934	8.412	8.943
beta_H[2,3]	10.021	0.132	9.761	10.023	10.280
beta_H[3,3]	9.612	0.162	9.310	9.609	9.945
beta_H[4,3]	-2.538	0.883	-4.318	-2.527	-0.834
beta_H[5,3]	4.007	0.619	2.738	4.025	5.195
beta_H[6,3]	8.150	1.216	6.522	7.773	10.760
beta_H[7,3]	-2.718	0.657	-4.040	-2.693	-1.476
beta_H[8,3]	5.238	0.401	4.665	5.197	6.022
beta_H[9,3]	-2.869	0.756	-4.402	-2.857	-1.401
beta_H[10,3]	8.662	0.275	8.126	8.666	9.202
beta_H[11,3]	8.564	0.279	7.950	8.588	9.051
beta_H[12,3]	5.245	0.321	4.479	5.289	5.786
beta_H[13,3]	8.811	0.175	8.466	8.814	9.153
beta_H[14,3]	5.702	0.275	5.094	5.719	6.189
beta_H[15,3]	10.367	0.313	9.746	10.373	11.006
beta_H[16,3]	6.675	0.450	5.687	6.717	7.439
beta_H[1,4]	8.174	0.191	7.758	8.190	8.511
beta_H[2,4]	10.042	0.134	9.760	10.049	10.286
beta_H[3,4]	10.099	0.161	9.745	10.111	10.382
beta_H[4,4]	11.784	0.452	10.880	11.802	12.652
beta_H[5,4]	5.653	0.752	4.421	5.554	7.399
beta_H[6,4]	7.140	0.898	5.157	7.421	8.341
beta_H[7,4]	8.288	0.356	7.571	8.292	8.971
beta_H[8,4]	6.746	0.222	6.337	6.744	7.153
beta_H[9,4]	7.191	0.478	6.240	7.199	8.149
beta_H[10,4]	7.703	0.231	7.272	7.693	8.164
beta_H[11,4]	9.406	0.200	9.011	9.410	9.783
beta_H[12,4]	7.153	0.209	6.756	7.152	7.582
beta_H[13,4]	9.003	0.137	8.711	9.007	9.264
beta_H[14,4]	7.710	0.223	7.300	7.704	8.154
beta_H[15,4]	9.463	0.227	9.020	9.463	9.909
beta_H[16,4]	9.246	0.200	8.886	9.236	9.666
beta_H[1,5]	8.959	0.151	8.660	8.965	9.254
beta_H[2,5]	10.764	0.097	10.580	10.762	10.960
beta_H[3,5]	10.888	0.163	10.593	10.879	11.235
beta_H[4,5]	8.378	0.467	7.483	8.373	9.312
beta_H[5,5]	5.502	0.582	4.090	5.565	6.486
beta_H[6,5]	8.979	0.642	8.073	8.816	10.475
beta_H[7,5]	6.773	0.337	6.113	6.772	7.443
beta_H[8,5]	8.237	0.191	7.899	8.227	8.617
beta_H[9,5]	8.217	0.480	7.291	8.223	9.148
beta_H[10,5]	10.087	0.224	9.630	10.085	10.518
beta_H[11,5]	11.538	0.226	11.097	11.539	11.980
beta_H[12,5]	8.505	0.195	8.134	8.502	8.903
beta_H[13,5]	9.997	0.129	9.750	9.996	10.249
beta_H[14,5]	9.185	0.230	8.766	9.175	9.670
beta_H[15,5]	11.160	0.240	10.683	11.161	11.624
beta_H[16,5]	9.946	0.159	9.610	9.950	10.254
beta_H[1,6]	10.230	0.197	9.885	10.218	10.661
beta_H[2,6]	11.532	0.109	11.313	11.531	11.749
beta_H[3,6]	10.810	0.157	10.469	10.818	11.098
beta_H[4,6]	12.865	0.822	11.210	12.893	14.422
beta_H[5,6]	6.003	0.611	4.885	5.974	7.219
beta_H[6,6]	8.847	0.663	7.094	8.985	9.782
beta_H[7,6]	9.888	0.587	8.720	9.886	11.050
beta_H[8,6]	9.540	0.248	9.072	9.548	9.950
beta_H[9,6]	8.450	0.807	6.877	8.460	10.083
beta_H[10,6]	9.493	0.316	8.801	9.512	10.056
beta_H[11,6]	10.815	0.351	10.075	10.836	11.442
beta_H[12,6]	9.373	0.249	8.899	9.358	9.889
beta_H[13,6]	11.021	0.173	10.709	11.012	11.401
beta_H[14,6]	9.834	0.292	9.233	9.838	10.392
beta_H[15,6]	10.844	0.422	10.000	10.844	11.665
beta_H[16,6]	10.528	0.210	10.074	10.538	10.917
beta_H[1,7]	10.906	0.956	8.378	11.040	12.418
beta_H[2,7]	12.242	0.448	11.331	12.250	13.123
beta_H[3,7]	10.533	0.681	8.996	10.597	11.672
beta_H[4,7]	2.443	4.259	-5.694	2.374	10.959
beta_H[5,7]	6.547	1.924	3.056	6.453	10.752
beta_H[6,7]	9.561	2.372	4.708	9.566	15.745
beta_H[7,7]	10.501	2.932	4.681	10.557	16.363
beta_H[8,7]	10.920	0.892	9.487	10.895	12.414
beta_H[9,7]	4.466	4.080	-3.572	4.418	12.610
beta_H[10,7]	9.856	1.440	7.207	9.772	12.920
beta_H[11,7]	10.957	1.737	7.791	10.836	14.886
beta_H[12,7]	9.952	0.902	7.867	10.028	11.444
beta_H[13,7]	11.612	0.810	9.656	11.708	12.839
beta_H[14,7]	10.417	0.936	8.314	10.472	12.030
beta_H[15,7]	11.800	2.195	7.599	11.769	16.190
beta_H[16,7]	11.939	1.097	10.222	11.785	14.542
beta0_H[1]	8.298	13.899	-22.456	8.489	35.813
beta0_H[2]	10.617	7.434	-4.774	10.766	25.068
beta0_H[3]	9.857	9.505	-8.902	9.904	28.471
beta0_H[4]	6.024	182.584	-369.722	4.302	373.358
beta0_H[5]	4.019	25.744	-44.859	4.225	55.155
beta0_H[6]	7.820	51.193	-103.758	7.639	126.084
beta0_H[7]	5.677	131.082	-268.435	7.898	263.415
beta0_H[8]	5.895	23.518	-15.122	6.523	24.557
beta0_H[9]	6.190	120.751	-241.425	7.685	244.666
beta0_H[10]	8.685	33.120	-57.508	8.505	76.129
beta0_H[11]	9.660	48.256	-92.833	10.595	105.677
beta0_H[12]	7.152	10.970	-13.978	6.975	30.150
beta0_H[13]	9.852	11.367	-10.629	9.780	31.214
beta0_H[14]	6.853	11.781	-15.113	6.860	29.506
beta0_H[15]	8.214	104.455	-207.886	10.100	214.133
beta0_H[16]	7.933	19.240	-29.640	8.026	46.894